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

3, 7, 9, 10, 14, 16, 17, 20, 21, 22, 24, 26, 30, 32, 33, 35, 39, 40, 41, 43, 46, 48, 51, 52, 53, 57, 61, 63, 68, 70, 71, 75, 80, 88, 97, 102, 104, 106, 107, 111, 115, 124, 125, 129, 133, 138, 142, 147, 151, 160, 162, 163, 164, 169, 173, 178, 180, 181, 189, 191, 193

Offset: 1

Author

Jon Perry, Jun 01 2003

Keywords

• nonn

Examples

			A000041(7)=15=0 mod 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000041, A087183, A243935.

Programs

Mathematica

Select[Range[250],Mod[PartitionsP[ # ],3]==0&] (* Zak Seidov, Apr 03 2007 *)

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","))) }

PARI

for(n=1,300,if(polcoeff(1/eta(x)+O(x^(n+1)),n)%3==0,print1(n,","))) \\ Benoit Cloitre, Oct 06 2005

PARI

is(n)=numbpart(n)%3==0 \\ Charles R Greathouse IV, Apr 08 2015

Formula

Conjecture : a(n) = 3n + o(n). - Benoit Cloitre, Oct 06 2005

A000041(a(n)) = A087183(n). - Zak Seidov, Apr 03 2007

Extensions

More terms from Benoit Cloitre, Oct 06 2005