The next number in the series: $0$, $0$, $2$, $6$, $12$, $21$, $34$, $51$












0












$begingroup$


I know that "next number" questions are not popular here, but this one is tough and I couldn't figure out the pattern. To give an idea one of the questions had a pattern of $operatorname{Prime}(operatorname{Fib}(n))$.



So this is the series:




$$0, 0, 2, 6, 12, 21, 34, 51$$
What is the next number in the series ?







sequences-and-series puzzle







share|cite|improve this question











$endgroup$








  • 3




    $begingroup$
    OEIS has nothing. Even when removing the initial $0$'s to account for possible different initial point.
    $endgroup$
    – Arthur
    Dec 5 '18 at 20:05








  • 2




    $begingroup$
    Could you give some context? Where did you see this question?
    $endgroup$
    – Kevin Long
    Dec 5 '18 at 20:07










  • $begingroup$
    My friend asked me this question, he said he saw it in a competition.
    $endgroup$
    – papabiceps
    Dec 5 '18 at 20:14






  • 4




    $begingroup$
    @papabiceps Ew, a "what's the next number" question in a competition? Yuck.
    $endgroup$
    – Frpzzd
    Dec 5 '18 at 21:02
















0












$begingroup$


I know that "next number" questions are not popular here, but this one is tough and I couldn't figure out the pattern. To give an idea one of the questions had a pattern of $operatorname{Prime}(operatorname{Fib}(n))$.



So this is the series:




$$0, 0, 2, 6, 12, 21, 34, 51$$
What is the next number in the series ?







sequences-and-series puzzle







share|cite|improve this question











$endgroup$








  • 3




    $begingroup$
    OEIS has nothing. Even when removing the initial $0$'s to account for possible different initial point.
    $endgroup$
    – Arthur
    Dec 5 '18 at 20:05








  • 2




    $begingroup$
    Could you give some context? Where did you see this question?
    $endgroup$
    – Kevin Long
    Dec 5 '18 at 20:07










  • $begingroup$
    My friend asked me this question, he said he saw it in a competition.
    $endgroup$
    – papabiceps
    Dec 5 '18 at 20:14






  • 4




    $begingroup$
    @papabiceps Ew, a "what's the next number" question in a competition? Yuck.
    $endgroup$
    – Frpzzd
    Dec 5 '18 at 21:02














0












0








0





$begingroup$


I know that "next number" questions are not popular here, but this one is tough and I couldn't figure out the pattern. To give an idea one of the questions had a pattern of $operatorname{Prime}(operatorname{Fib}(n))$.



So this is the series:




$$0, 0, 2, 6, 12, 21, 34, 51$$
What is the next number in the series ?







sequences-and-series puzzle







share|cite|improve this question











$endgroup$




I know that "next number" questions are not popular here, but this one is tough and I couldn't figure out the pattern. To give an idea one of the questions had a pattern of $operatorname{Prime}(operatorname{Fib}(n))$.



So this is the series:




$$0, 0, 2, 6, 12, 21, 34, 51$$
What is the next number in the series ?







sequences-and-series puzzle




sequences-and-series puzzle






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 5 '18 at 20:55









Blue

48.7k870156




48.7k870156










asked Dec 5 '18 at 20:03









papabicepspapabiceps

322113




322113








  • 3




    $begingroup$
    OEIS has nothing. Even when removing the initial $0$'s to account for possible different initial point.
    $endgroup$
    – Arthur
    Dec 5 '18 at 20:05








  • 2




    $begingroup$
    Could you give some context? Where did you see this question?
    $endgroup$
    – Kevin Long
    Dec 5 '18 at 20:07










  • $begingroup$
    My friend asked me this question, he said he saw it in a competition.
    $endgroup$
    – papabiceps
    Dec 5 '18 at 20:14






  • 4




    $begingroup$
    @papabiceps Ew, a "what's the next number" question in a competition? Yuck.
    $endgroup$
    – Frpzzd
    Dec 5 '18 at 21:02














  • 3




    $begingroup$
    OEIS has nothing. Even when removing the initial $0$'s to account for possible different initial point.
    $endgroup$
    – Arthur
    Dec 5 '18 at 20:05








  • 2




    $begingroup$
    Could you give some context? Where did you see this question?
    $endgroup$
    – Kevin Long
    Dec 5 '18 at 20:07










  • $begingroup$
    My friend asked me this question, he said he saw it in a competition.
    $endgroup$
    – papabiceps
    Dec 5 '18 at 20:14






  • 4




    $begingroup$
    @papabiceps Ew, a "what's the next number" question in a competition? Yuck.
    $endgroup$
    – Frpzzd
    Dec 5 '18 at 21:02








3




3




$begingroup$
OEIS has nothing. Even when removing the initial $0$'s to account for possible different initial point.
$endgroup$
– Arthur
Dec 5 '18 at 20:05






$begingroup$
OEIS has nothing. Even when removing the initial $0$'s to account for possible different initial point.
$endgroup$
– Arthur
Dec 5 '18 at 20:05






2




2




$begingroup$
Could you give some context? Where did you see this question?
$endgroup$
– Kevin Long
Dec 5 '18 at 20:07




$begingroup$
Could you give some context? Where did you see this question?
$endgroup$
– Kevin Long
Dec 5 '18 at 20:07












$begingroup$
My friend asked me this question, he said he saw it in a competition.
$endgroup$
– papabiceps
Dec 5 '18 at 20:14




$begingroup$
My friend asked me this question, he said he saw it in a competition.
$endgroup$
– papabiceps
Dec 5 '18 at 20:14




4




4




$begingroup$
@papabiceps Ew, a "what's the next number" question in a competition? Yuck.
$endgroup$
– Frpzzd
Dec 5 '18 at 21:02




$begingroup$
@papabiceps Ew, a "what's the next number" question in a competition? Yuck.
$endgroup$
– Frpzzd
Dec 5 '18 at 21:02










1 Answer
1






active

oldest

votes


















0












$begingroup$

I'll find some pattern and then claim a correct answer:



0, 0, 2, 6, 12, 21, 34, 51



0, 2, 4, 6, 9, 13, 17



2, 2, 2, 3, 4, 4


Then 4 + 17 = 21 and 21 + 51 = 72 .



Well, {2, 2, 2, 3, 4, 4} calls for {2, 2, 2, 3, 4, 4, 4} but a continuing pattern is debatable after that. It might be {2, 2, 2, 3, 4, 4, 4, 5, ...}.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Can you elaborate?
    $endgroup$
    – johnnycrab
    Dec 5 '18 at 20:53










  • $begingroup$
    @johnnycrab Binomial transform. But not very convincing here.
    $endgroup$
    – Jean-Claude Arbaut
    Dec 5 '18 at 21:15












  • $begingroup$
    @Jean-Claude Arbaut Thanks, didn't see it from just looking at the numbers.
    $endgroup$
    – johnnycrab
    Dec 5 '18 at 21:18











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









0












$begingroup$

I'll find some pattern and then claim a correct answer:



0, 0, 2, 6, 12, 21, 34, 51



0, 2, 4, 6, 9, 13, 17



2, 2, 2, 3, 4, 4


Then 4 + 17 = 21 and 21 + 51 = 72 .



Well, {2, 2, 2, 3, 4, 4} calls for {2, 2, 2, 3, 4, 4, 4} but a continuing pattern is debatable after that. It might be {2, 2, 2, 3, 4, 4, 4, 5, ...}.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Can you elaborate?
    $endgroup$
    – johnnycrab
    Dec 5 '18 at 20:53










  • $begingroup$
    @johnnycrab Binomial transform. But not very convincing here.
    $endgroup$
    – Jean-Claude Arbaut
    Dec 5 '18 at 21:15












  • $begingroup$
    @Jean-Claude Arbaut Thanks, didn't see it from just looking at the numbers.
    $endgroup$
    – johnnycrab
    Dec 5 '18 at 21:18
















0












$begingroup$

I'll find some pattern and then claim a correct answer:



0, 0, 2, 6, 12, 21, 34, 51



0, 2, 4, 6, 9, 13, 17



2, 2, 2, 3, 4, 4


Then 4 + 17 = 21 and 21 + 51 = 72 .



Well, {2, 2, 2, 3, 4, 4} calls for {2, 2, 2, 3, 4, 4, 4} but a continuing pattern is debatable after that. It might be {2, 2, 2, 3, 4, 4, 4, 5, ...}.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Can you elaborate?
    $endgroup$
    – johnnycrab
    Dec 5 '18 at 20:53










  • $begingroup$
    @johnnycrab Binomial transform. But not very convincing here.
    $endgroup$
    – Jean-Claude Arbaut
    Dec 5 '18 at 21:15












  • $begingroup$
    @Jean-Claude Arbaut Thanks, didn't see it from just looking at the numbers.
    $endgroup$
    – johnnycrab
    Dec 5 '18 at 21:18














0












0








0





$begingroup$

I'll find some pattern and then claim a correct answer:



0, 0, 2, 6, 12, 21, 34, 51



0, 2, 4, 6, 9, 13, 17



2, 2, 2, 3, 4, 4


Then 4 + 17 = 21 and 21 + 51 = 72 .



Well, {2, 2, 2, 3, 4, 4} calls for {2, 2, 2, 3, 4, 4, 4} but a continuing pattern is debatable after that. It might be {2, 2, 2, 3, 4, 4, 4, 5, ...}.






share|cite|improve this answer











$endgroup$



I'll find some pattern and then claim a correct answer:



0, 0, 2, 6, 12, 21, 34, 51



0, 2, 4, 6, 9, 13, 17



2, 2, 2, 3, 4, 4


Then 4 + 17 = 21 and 21 + 51 = 72 .



Well, {2, 2, 2, 3, 4, 4} calls for {2, 2, 2, 3, 4, 4, 4} but a continuing pattern is debatable after that. It might be {2, 2, 2, 3, 4, 4, 4, 5, ...}.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Dec 5 '18 at 21:11

























answered Dec 5 '18 at 20:50









S SpringS Spring

1723




1723












  • $begingroup$
    Can you elaborate?
    $endgroup$
    – johnnycrab
    Dec 5 '18 at 20:53










  • $begingroup$
    @johnnycrab Binomial transform. But not very convincing here.
    $endgroup$
    – Jean-Claude Arbaut
    Dec 5 '18 at 21:15












  • $begingroup$
    @Jean-Claude Arbaut Thanks, didn't see it from just looking at the numbers.
    $endgroup$
    – johnnycrab
    Dec 5 '18 at 21:18


















  • $begingroup$
    Can you elaborate?
    $endgroup$
    – johnnycrab
    Dec 5 '18 at 20:53










  • $begingroup$
    @johnnycrab Binomial transform. But not very convincing here.
    $endgroup$
    – Jean-Claude Arbaut
    Dec 5 '18 at 21:15












  • $begingroup$
    @Jean-Claude Arbaut Thanks, didn't see it from just looking at the numbers.
    $endgroup$
    – johnnycrab
    Dec 5 '18 at 21:18
















$begingroup$
Can you elaborate?
$endgroup$
– johnnycrab
Dec 5 '18 at 20:53




$begingroup$
Can you elaborate?
$endgroup$
– johnnycrab
Dec 5 '18 at 20:53












$begingroup$
@johnnycrab Binomial transform. But not very convincing here.
$endgroup$
– Jean-Claude Arbaut
Dec 5 '18 at 21:15






$begingroup$
@johnnycrab Binomial transform. But not very convincing here.
$endgroup$
– Jean-Claude Arbaut
Dec 5 '18 at 21:15














$begingroup$
@Jean-Claude Arbaut Thanks, didn't see it from just looking at the numbers.
$endgroup$
– johnnycrab
Dec 5 '18 at 21:18




$begingroup$
@Jean-Claude Arbaut Thanks, didn't see it from just looking at the numbers.
$endgroup$
– johnnycrab
Dec 5 '18 at 21:18


















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