0,3

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 6, 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 (jvospost3(AT)gmail.com), Jun 18 2005

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

A000009(n) is odd iff n is of the form k*(3*k - 1)/2 or k*(3*k + 1)/2. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 18 2005

a(n) = A000009(A001318(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 22 2006

Cf. A000009, A035359, A051005.

Cf. A118303.

Sequence in context: A053351 A146244 A146457 this_sequence A003536 A118173 A079450

Adjacent sequences: A051041 A051042 A051043 this_sequence A051045 A051046 A051047

nonn

Eric Weisstein (eric(AT)weisstein.com)