

A110996


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


1




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

Table of n, a(n) for n=1..5.


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

Cf. A007504, A014284, A110979, A264858.
Sequence in context: A268874 A264223 A233343 * A013769 A013899 A075268
Adjacent sequences: A110993 A110994 A110995 * A110997 A110998 A110999


KEYWORD

nonn


AUTHOR

Walter Kehowski, Sep 30 2005


EXTENSIONS

New term 1 prepended by Altug Alkan, Nov 29 2015


STATUS

approved



