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

1,1

Links

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

Formula

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

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

Example

A000041(7)=15=0 mod 3.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000041, A087183, A243935.

Sequence in context: A339618 A357707 A294571 * A091210 A333911 A276492

Adjacent sequences: A083211 A083212 A083213 * A083215 A083216 A083217

Keyword

nonn

Author

Jon Perry, Jun 01 2003

Extensions

More terms from Benoit Cloitre, Oct 06 2005

Status

approved