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A051044 Odd values of the PartitionsQ function A000009. 3
1, 1, 3, 5, 15, 27, 89, 165, 585, 1113, 4097, 7917, 29927, 58499, 225585, 444793, 1741521, 3457027, 13699699, 27342421, 109420549, 219358315, 884987529, 1780751883, 7233519619, 14600965705, 59656252987, 120742510607 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A000009(n) is odd iff n is of the form k*(3*k - 1)/2 or k*(3*k + 1)/2. - Jonathan Vos Post, Jun 18 2005

Eric W. Weisstein comments: "The values of n for which a(n) is prime are 3, 4, 5, 7, 22, 70, 100, 495, 1247, 2072, 320397, ... (A035359), with no others for n <= 3015000 (Weisstein, May 06 2000). These values correspond to 2, 2, 3, 5, 89, 29927, 444793, 602644050950309, ... (A051005). It is not known if a(n) is infinitely often prime, but Gordon and Ono (1997) proved that it is 'almost always' divisible by any given power of 2 (1997)."

Semiprime odd values of the PartitionsQ function A000009 begin: a(4) = 15 = 3 * 5, a(10) = 4097 = 17 * 241, a(19) = 27342421 = 389 * 70289, a(23) = 1780751883 = 3 * 593583961, a(27) = 120742510607 = 31 * 3894919697. - Jonathan Vos Post, Jun 18 2005

LINKS

Table of n, a(n) for n=0..27.

Eric Weisstein's World of Mathematics, Partition Function Q Congruences

FORMULA

a(n) = A000009(A001318(n)). - Reinhard Zumkeller, Apr 22 2006

MATHEMATICA

PartitionsQ /@ Table[n*((n + 1)/6), {n, Select[Range[50], Mod[#, 3] != 1 & ]}] (* Jean-Fran├žois Alcover, Oct 31 2012, after Reinhard Zumkeller *)

CROSSREFS

Cf. A000009, A035359, A051005, A118303.

Sequence in context: A274638 A146244 A146457 * A003536 A284031 A284410

Adjacent sequences:  A051041 A051042 A051043 * A051045 A051046 A051047

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified July 14 21:29 EDT 2020. Contains 335729 sequences. (Running on oeis4.)