A162848 An alternating 2-based sum from prime(n) up to the base of the n-th Mersenne prime.

0, 5, 7, 9, 18, 25, 24, 51, 120, 181, 223, 264, 1243, 1455, 3129, 5430, 5616, 7953, 10534, 10953, 24115, 24736, 27910, 49711, 54109, 57873, 111090, 215449, 276096, 329955, 540039, 1891903, 2148379, 3144261, 3495451, 7440328, 7553209, 17431240, 33667044

Offset

1,2

Comments

Define a 2-based sum S(l,u) = Sum_{j=l..u} (2 - j*(-1)^j). Then a(n) is this sum evaluated with a lower limit l = A000040(n) = prime(n) and with an upper limit u = A000043(n).

Links

Table of n, a(n) for n=1..39.

Formula

a(n) = Sum_{j=A000040(n)..A000043(n)} (2 - j*(-1)^j).

Example

a(1) = 2 - 2 = 0;
a(2) = 2 + 3 = 5;
a(3) = 2 + 5 = 7;
a(4) = 2 + 7 = 9;
a(5) = 2 + 11 + 2 - 12 + 2 + 13 = 18.

Maple

A152832 := proc(n) (n+1)/2-(9*(-1)^n+1)/4 ; end:
S := proc(u) 2*u-(-1)^u*A152832(u) ; end:
A000043 := proc(n) op(n, [ 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607,
1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497,
86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917 ]) ; end:
A162848 := proc(n) S( A000043(n))-S(ithprime(n)-1) ; end: seq(A162848(n), n=1..39) ; # R. J. Mathar, Aug 14 2009

Crossrefs

Cf. A000040, A000043, A162938.

Sequence in context: A036708 A124822 A072180 * A259359 A024571 A186406

Adjacent sequences: A162845 A162846 A162847 * A162849 A162850 A162851

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 21 2009

Extensions

Corrected from a(8) on by R. J. Mathar, Aug 14 2009

Status

approved