1,1

I have checked out to the first 250000 primes but the last entry is at the 504th prime, 3607.

a(n)=sum(prime(j), j=1..N_n)-1 and a(n) is a power.

Since sum(prime(j),j=1..10)=129, 128=2^7.

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 p:=ithprime(n); [n, s(n-1)[2]+p] fi end; t := proc(n) option remember; [n, s(n)[2]-1] 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;

s = 0; Do[s = s + Prime[n]; If[GCD @@ Transpose[ FactorInteger[s - 1]][[2]] > 1, Print[s - 1]], {n, 10^6}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 02 2005)

Cf. A007504, A110979.

Sequence in context: A132074 A137354 A113495 this_sequence A001640 A073141 A093175

Adjacent sequences: A110994 A110995 A110996 this_sequence A110998 A110999 A111000

nonn

Walter A. Kehowski (wkehowski(AT)cox.net), Sep 30 2005