A376890 Alternating sum of twin primes (A001097).

3, -2, 5, -6, 7, -10, 9, -20, 11, -30, 13, -46, 15, -56, 17, -84, 19, -88, 21, -116, 23, -126, 25, -154, 27, -164, 29, -168, 31, -196, 33, -206, 35, -234, 37, -244, 39, -272, 41, -306, 43, -376, 45, -386, 47, -414, 49, -472, 51, -518, 53, -546, 55, -562, 57, -584, 59, -600, 61, -748

Offset: 1

Author

Ilya Gutkovskiy, Oct 08 2024

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Twin Primes.

Crossrefs

Cf. A001097, A008347, A048598.

Programs

Maple

T1:= select(t -> isprime(t) and isprime(t+2), [seq(i,i=5..1000,6)]):
T:= map(t -> (-t, t+2), T1): T:= [3,op(T)]:
ListTools:-PartialSums(T); # Robert Israel, Nov 08 2024

Formula

a(n) = Sum_{k=1..n} (-1)^(k+1) * A001097(k).

a(2*n-1) = 2*n+1.