A066033 Alternating sum of primes: a(1) = A000040(1) = 2 and a(n) = a(n-1) + A000040(n)*(-1)^n for n > 1.

2, 5, 0, 7, -4, 9, -8, 11, -12, 17, -14, 23, -18, 25, -22, 31, -28, 33, -34, 37, -36, 43, -40, 49, -48, 53, -50, 57, -52, 61, -66, 65, -72, 67, -82, 69, -88, 75, -92, 81, -98, 83, -108, 85, -112, 87, -124, 99, -128, 101, -132, 107, -134, 117, -140, 123, -146, 125, -152, 129, -154, 139, -168, 143, -170, 147, -184, 153

Offset: 1

Author

Reinhard Zumkeller, Dec 12 2001

Keywords

• sign

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A007504, A008347, A000040.

Programs

Maple

ListTools:-PartialSums([2,seq((-1)^n*ithprime(n),n=2..100)]); # Robert Israel, Jun 14 2016

Mathematica

4 + Accumulate[Table[Prime[n](-1)^(n), {n, 1, 70}]] (* Terry D. Grant, Jun 14 2016 *)

PARI

{ for (n=1, 1000, if (n==1, a=2, a+=prime(n)*(-1)^n); write("b066033.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 07 2009

Formula

a(n) = 4 + (-1)^n*A008347(n). - Robert Israel, Jun 14 2016