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A083214
Numbers k for which 3 | p(k), where p(k) = A000041(k) is the k-th partition number.
7
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
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
KEYWORD
nonn
AUTHOR
Jon Perry, Jun 01 2003
EXTENSIONS
More terms from Benoit Cloitre, Oct 06 2005
STATUS
approved