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.
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(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;
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
Walter Kehowski, Sep 30 2005
EXTENSIONS
New term 1 prepended by Altug Alkan, Nov 29 2015
a(6) from Jinyuan Wang, Aug 09 2023
STATUS
approved