A136288 Primes which are the absolute value of the alternating sum and difference of the first n primes.

2, 3, 5, 7, 13, 19, 29, 53, 61, 71, 79, 83, 97, 103, 113, 139, 149, 151, 157, 163, 167, 191, 199, 233, 251, 281, 337, 347, 353, 397, 421, 433, 461, 563, 599, 643, 719, 773, 797, 811, 859, 883, 953, 977, 1031, 1039, 1061, 1063, 1091, 1097, 1153, 1187, 1201, 1213

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 20 2008

Keywords

• easy
• nonn

Examples

			5 = abs(2-3+5-7+11-13) (first 6 primes),
7 = abs(2-3+5-7+11-13+17-19) (first 8 primes),
etc.
		

Links

• Dmitry Kamenetsky, Table of n, a(n) for n = 1..10000 (first 144 terms by Paolo P. Lava and Giorgio Balzarotti)

Crossrefs

Cf. A000040, A008347, A013918.

Programs

Maple

P:=proc(n) local i,s; s:=0; for i from 1 by 1 to n do s:=s+(-1)^i*ithprime(i); if isprime(abs(s)) then print(abs(s)); fi; od; end: P(1000);

Mathematica

Select[Abs@Accumulate@Table[(-1)^(k+1)*Prime@k,{k,355}],PrimeQ] (* Giorgos Kalogeropoulos, Sep 22 2021 *)

Formula

A000040 INTERSECT A008347. - R. J. Mathar, Apr 04 2008