A378677 a(n)=a(n-1) + prime(n) for n prime, and a(n)=-a(n-1) otherwise, with a(0)=0, with duplicates removed afterwards.

0, 3, 8, -8, -3, 14, -14, 17, -17, 24, -24, 35, -35, 32, -32, 51, -51, 58, -58, 69, -69, 88, -88, 91, -91, 100, -100, 111, -111, 130, -130, 147, -147, 136, -136, 195, -195, 158, -158, 209, -209, 192, -192, 239, -239, 222, -222, 287, -287, 260, -260, 303, -303

Offset: 0

Author

Bill McEachen, Dec 03 2024

Keywords

• sign

Comments

Let b = subset of positive terms for n>4. We have A073131= b(m+2)-b(m) , A006450= b(m+2)+b(m) and A299644= b(m+2)+2*b(m+1)+b(m).

Examples

			n=1 is not prime, so a(1)= -a(0)= 0. n=2 is prime, so a(2)=a(1)+prime(2)=0+3=3. n=5 is prime, so a(5)=3, but note that it duplicates a(2). n=6 is not prime, so a(6)= -a(5)=-3. After terms are computed, duplicates are only then removed, which will alter indices accordingly.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A006450, A073131, A299644.

Programs

Mathematica

Module[{n = 0}, DeleteDuplicates[NestList[If[PrimeQ[++n], # + Prime[n], -#] &, 0, 200]]] (* Paolo Xausa, Dec 06 2024 *)

Formula

a(n) = a(n-1) + a prime for n odd >4.

a(n) = -a(n-1) for a(n-1)>0, n>1.