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

1,2

Comments

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

Links

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

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

Example

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]

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 *)

Prog

(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, ", ")))

Crossrefs

Cf. A008347, A077126, A077131.

Sequence in context: A291867 A219674 A075571 * A164642 A247633 A357170

Adjacent sequences: A077130 A077131 A077132 * A077134 A077135 A077136

Keyword

nonn

Author

Jon Perry, Nov 29 2002

Extensions

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

Name clarified by Paolo Xausa, Apr 12 2023

Status

approved