A110996 Powers equal to (sum of first k primes) plus 1, for some k >= 0.

1, 441, 970225, 1464100, 194379364, 1303400915339554201

Offset: 1

Author

Walter Kehowski, Sep 30 2005

Keywords

• nonn
• more

Comments

I have checked for powers out to the 250000th prime and the last element found is at the 6420th prime, 64067. It is interesting to note that the only powers so far are squares. Finding a higher power would be interesting.

Examples

			1 is a term (corresponding to k=0), since it is the empty sum plus 1. - _N. J. A. Sloane_, Dec 02 2015
441 is a term since sum(primes<=59) = 440 and 441 = 21^2.
		

Crossrefs

Cf. A007504, A110979, A110997, A264858.

Intersection of A001597 and A014284.

Programs

Maple

with(numtheory); egcd := proc(n) local L; L:=map(proc(z) z[2] end, ifactors(n)[2]); igcd(op(L)) end: s := proc(n) option remember; local p; if n=1 then [1,2] else [n,s(n-1)[2]+ithprime(n)] fi end; t := proc(n) option remember; [n,s(n)[2]+1] fi end; PW:=[]; for z to 1 do for j from 1 to 250000 do if egcd(t(j)[2])>1 then PW:=[op(PW),t(j)] fi od od; PW;

PARI

lista(nn) = { print1(1, ", "); s = 1; for(k=1, nn, s += prime(k); if(ispower(s) || s==1, print1(s, ", ")););} \\ Altug Alkan, Nov 29 2015

Extensions

New term 1 prepended by Altug Alkan, Nov 29 2015

a(6) from Jinyuan Wang, Aug 09 2023