A129491 Digital sum of the 2^n-th partition number.

1, 2, 5, 4, 6, 24, 22, 34, 83, 120, 152, 145, 286, 477, 561, 796, 1271, 1639, 2471, 3598, 5114, 7221, 10283, 14315, 20585, 29110, 40890, 58834, 82319, 115690, 164128, 232044, 328463, 462853, 657811, 927235, 1311605, 1855787, 2629927, 3708205

Offset: 0

Author

Robert G. Wilson v, Apr 12 2007

Keywords

• base
• nonn

Comments

For the same sequence but for base 10 (A070177): 1,6,43,143,471,1511,4959,15914,49580,158148,501883,1582908,5014367,....

Examples

			a(9) = 120 since P(2^9) = 4453575699570940947378 and 4+4+5+3+5+7+5+6+9+9+5+7+0+9+4+0+9+4+7+3+7+8 = 120.
		

Crossrefs

Cf. A000041, A000079, A007953, A068413, A129490.

Programs

Mathematica

f[n_] := Plus @@ IntegerDigits @PartitionsP[2^n]; Table[ f@n, {n, 0, 42}]

Formula

a(n) = A007953(A000041(A000079(n))) = A007953(A068413(n)).

a(n) =~ 9*A129490(n)/2.

Extensions

Offset corrected by Alois P. Heinz, Sep 20 2024