A077133 a(n) is the difference between the sum of the first n even-indexed primes and the sum of the first n odd-indexed primes.

1, 3, 5, 7, 13, 19, 21, 27, 29, 33, 39, 45, 49, 53, 57, 61, 63, 65, 71, 77, 79, 81, 83, 95, 97, 103, 113, 119, 121, 125, 135, 139, 143, 149, 151, 157, 163, 167, 175, 183, 185, 187, 191, 199, 201, 213, 217, 221, 233, 251, 261, 267, 273, 279, 281, 287, 289, 299

Offset: 1

Author

Jon Perry, Nov 29 2002

Keywords

• nonn

Comments

Some odd numbers such as 11, 17, 23 and 25 never appear.

Examples

			a(2) = 3 as the sum of the first 2 even-indexed primes is prime(2) + prime(4) = 3 + 7 = 10, the sum of the first 2 odd-indexed primes is prime(1) + prime(3) = 2 + 5 = 7 and 10 - 7 = 3. [edited by _Paolo Xausa_, Apr 12 2023]
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008347, A077126, A077131.

Programs

Maple

with(numtheory): A008347 := proc(n) option remember; if n = 0 then 0 else abs(A008347(n-1)-ithprime(n)); fi; end proc:
seq(A008347(2n),n=1..80); # Ridouane Oudra, Aug 31 2019

Mathematica

Table[ Sum[ Prime[2i], {i, 1, n}] - Sum[ Prime[2i - 1], {i, 1, n}], {n, 1, 60}]
A077133[nmax_]:=Accumulate[Prime[Range[2,2nmax,2]]-Prime[Range[1,2nmax,2]]];A077133[100] (* Paolo Xausa, Apr 12 2023 *)

PARI

my(pc=1, p1s=0, p2s=0); forprime (p=2, 500, pc=!pc; if (pc, p1s+=p, p2s+=p); if (pc,print1(p1s-p2s, ", ")))

Formula

a(n) = Sum_{i=0..n-1} (prime(2*i+2) - prime(2*i+1)).

a(n) = A008347(2n). - Ridouane Oudra, Aug 31 2019

a(n) = A077126(n) - A077131(n). - Michel Marcus, Oct 05 2019

Extensions

Edited and extended by Robert G. Wilson v, Nov 30 2002

Name clarified by Paolo Xausa, Apr 12 2023