

A110996


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


3




OFFSET

1,2


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.


LINKS



EXAMPLE

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.


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(n1)[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;


PROG

(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


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



