A110997 -id:A110997 - cp's OEIS frontend

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

1, 441, 970225, 1464100, 194379364, 1303400915339554201

Offset: 1

Walter Kehowski, Sep 30 2005

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.

			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.

Cf. A007504, A110979, A110997, A264858.

Intersection of A001597 and A014284.

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;

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

New term 1 prepended by Altug Alkan, Nov 29 2015

a(6) from Jinyuan Wang, Aug 09 2023

A110979 Squares equal to the sum of the first k primes minus 1.

Original entry on oeis.org

1, 4, 9, 16, 196, 839056, 7796654478001

Offset: 1

Giovanni Teofilatto, Sep 30 2005

No more terms < 7472966967498, sum of first 10^6 primes minus 1. - Ray Chandler, Oct 07 2005

Cf. A007504, A110997.

Intersection of A000290 and A237589.

Select[Accumulate[Prime[Range[1000]]]-1,IntegerQ[Sqrt[#]]&] (* Harvey P. Dale, Jun 09 2022 *)

lista(nn) = my(s=-1); forprime(p=2, nn, s+=p; if(issquare(s), print1(s, ", "))) \\ Jinyuan Wang, Aug 10 2023

a(6) corrected by Ray Chandler, Oct 07 2005

a(7) from Jinyuan Wang, Aug 10 2023

cp's OEIS Frontend

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

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