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

%I A083214 #19 May 21 2022 08:42:43
%S A083214 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 A083214 53,57,61,63,68,70,71,75,80,88,97,102,104,106,107,111,115,124,125,129,
%U A083214 133,138,142,147,151,160,162,163,164,169,173,178,180,181,189,191,193
%N A083214 Numbers k for which 3 | p(k), where p(k) = A000041(k) is the k-th partition number.
%H A083214 Amiram Eldar, <a href="/A083214/b083214.txt">Table of n, a(n) for n = 1..1000</a>
%F A083214 Conjecture : a(n) = 3n + o(n). - _Benoit Cloitre_, Oct 06 2005
%F A083214 A000041(a(n)) = A087183(n). - _Zak Seidov_, Apr 03 2007
%e A083214 A000041(7)=15=0 mod 3.
%t A083214 Select[Range[250],Mod[PartitionsP[ # ],3]==0&] (* _Zak Seidov_, Apr 03 2007 *)
%o A083214 (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 A083214 (PARI) for(n=1,300,if(polcoeff(1/eta(x)+O(x^(n+1)),n)%3==0,print1(n,","))) \\ _Benoit Cloitre_, Oct 06 2005
%o A083214 (PARI) is(n)=numbpart(n)%3==0 \\ _Charles R Greathouse IV_, Apr 08 2015
%Y A083214 Cf. A000041, A087183, A243935.
%K A083214 nonn
%O A083214 1,1
%A A083214 _Jon Perry_, Jun 01 2003
%E A083214 More terms from _Benoit Cloitre_, Oct 06 2005