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

%I

%S 1,441,970225,1464100,194379364

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

%C 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.

%e 1 is a term (corresponding to k=0), since it is the empty sum plus 1. - _N. J. A. Sloane_, Dec 02 2015

%e 441 is a term since sum(primes<=59) = 440 and 441 = 21^2.

%p 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;

%o (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

%Y Cf. A007504, A014284, A110979, A264858.

%K nonn

%O 1,2

%A _Walter Kehowski_, Sep 30 2005

%E New term 1 prepended by _Altug Alkan_, Nov 29 2015

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Last modified July 25 11:23 EDT 2021. Contains 346289 sequences. (Running on oeis4.)