A237277 -id:A237277 - cp's OEIS frontend

A237276 Numbers k such that A000041(k) == 1 (mod 3).

0, 1, 5, 8, 18, 19, 23, 27, 28, 34, 36, 37, 44, 45, 50, 54, 55, 59, 62, 64, 72, 73, 77, 81, 82, 86, 89, 91, 95, 98, 99, 100, 110, 112, 113, 116, 117, 118, 119, 122, 128, 134, 137, 139, 140, 143, 146, 148, 149, 150, 152, 154, 155, 157, 158, 161, 166, 168, 170

Offset: 1

Clark Kimberling, Feb 05 2014

The set of positive integers is partitioned by A083214, A237276, and A237277.

			A000041(8) = 22 == 1 (mod 3).

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Clark Kimberling)

Cf. A000041, A083214, A237276, A237277.

f[n_, k_] := Select[Range[0, 250], Mod[PartitionsP[#], n] == k &]
Table[f[3, k], {k, 0, 2}] (* A083214, A237276, A237277 *)
Table[f[4, k], {k, 0, 3}] (* A237278-A237281 *)

a(1)=0 inserted by Amiram Eldar, May 22 2025

A087185 Partition numbers of the form 3*k+2.

Original entry on oeis.org

2, 5, 11, 56, 77, 101, 176, 1958, 4565, 6842, 26015, 53174, 124754, 173525, 526823, 715220, 966467, 2012558, 2323520, 2679689, 3554345, 7089500, 9289091, 12132164, 13848650, 23338469, 26543660, 30167357, 38887673, 56634173

Offset: 1

Reinhard Zumkeller, Aug 23 2003

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Partition Function.
Eric Weisstein's World of Mathematics, Partition Function P Congruences.

Cf. A000041, A087182, A087183, A087184, A068907, A052001, A052003, A237277.

Select[PartitionsP[Range[200]],Divisible[#-2,3]&] (* Harvey P. Dale, Apr 22 2016 *)

a(n) = A000041(A237277(n)). - Amiram Eldar, May 22 2025

cp's OEIS Frontend

A237276 Numbers k such that A000041(k) == 1 (mod 3).

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