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A110996 Powers equal to (sum of first k primes) plus 1, for some k >= 0. 3
1, 441, 970225, 1464100, 194379364, 1303400915339554201 (list; graph; refs; listen; history; text; internal format)
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(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
Intersection of A001597 and A014284.
Sequence in context: A268874 A264223 A233343 * A013769 A013899 A075268
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

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Last modified June 12 14:10 EDT 2024. Contains 373331 sequences. (Running on oeis4.)