A162385 Alternating sum from the n-th Mersenne prime up to the n-th perfect number.

2, 11, 233, 4001, 16771073, 4294868993, 68719083521, 1152921502996234241, 1329227995784915871174424803370074113, 95780971304118053647396688732666809244153592049303553

Offset

1,1

Comments

Define the alternating sum S(k) = sum_{x=0..k} x*(-1)^x = (-1)^k*(k/2+1/4)-1/4 = A130472(k).

a(n) is this sum evaluated with a lower limit of A000668(n) and an upper limit of A000396(n).

Links

Table of n, a(n) for n=1..10.

Formula

a(n) = A130472(A000396(n)) - A130472( A000668(n)-1).

a(n) = (A000396(n) - A000668(n) + 1)/2. - César Aguilera, May 13 2017

a(n) = (1 + A139224(n))/2. - Omar E. Pol, May 22 2017

Example

a(1) = -3+4-5+6 = 2. a(2) = -7+8-9+10-11+12-13+14-15+16-17+...-27+28 = 11.

Crossrefs

Cf. A000396, A000668.

Sequence in context: A042805 A088639 A269710 * A244012 A264330 A343898

Adjacent sequences: A162382 A162383 A162384 * A162386 A162387 A162388

Keyword

nonn,less

Author

Juri-Stepan Gerasimov, Jul 21 2009

Extensions

Edited and extended by R. J. Mathar, Sep 16 2009

Status

approved