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A083214 Numbers n for which 3 | p(n), where p(n) = A000041(n) is the n-th partition number. 6

%I

%S 3,7,9,10,14,16,17,20,21,22,24,26,30,32,33,35,39,40,41,43,46,48,51,52,

%T 53,57,61,63,68,70,71,75,80,88,97,102,104,106,107,111,115,124,125,129,

%U 133,138,142,147,151,160,162,163,164,169,173,178,180,181,189,191,193

%N Numbers n for which 3 | p(n), where p(n) = A000041(n) is the n-th partition number.

%F Conjecture : a(n)=3n+o(n). - _Benoit Cloitre_, Oct 06 2005

%F A000041(a(n)) = A087183(n). - _Zak Seidov_, Apr 03 2007

%e A000041(7)=15=0 mod 3.

%t Select[Range[250],Mod[PartitionsP[ # ],3]==0&] - _Zak Seidov_, Apr 03 2007

%o (PARI) { v=[1,1,2,3,5,7,11,15,22,30,42,56,77,101,135,176,231,297,385,490,627,792,1002,1255,1575,1958,2436,3010,3718,4565,5604,6842,8349,10143,12310,14883,17977,21637,26015,31185,37338,44583,53174,63261,75175,89134]; for (i=2,length(v)-1,if (v[i]%3==0,print1(i-1","))) }

%o (PARI) for(n=1,300,if(polcoeff(1/eta(x)+O(x^(n+1)),n)%3==0,print1(n,","))) \\ Cloitre

%o (PARI) is(n)=numbpart(n)%3==0 \\ _Charles R Greathouse IV_, Apr 08 2015

%Y Cf. A000041, A087183, A243935.

%K nonn

%O 1,1

%A _Jon Perry_, Jun 01 2003

%E More terms from _Benoit Cloitre_, Oct 06 2005

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Last modified July 11 23:53 EDT 2020. Contains 335654 sequences. (Running on oeis4.)