This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A110997 #19 Aug 12 2023 01:15:54
%S A110997 1,4,9,16,27,128,196,839056,7796654478001
%N A110997 Powers equal to (sum of first k primes) minus 1.
%C A110997 I have checked out to the first 250000 primes but the last entry is at the 504th prime, 3607.
%e A110997 128 is a term because 128 = -1 + Sum_{i=1..10} prime(i) = 2^7.
%p A110997 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 or t(j)[2]=1 then PW:=[op(PW),t(j)] fi od od; PW;
%t A110997 s = 0; Do[s = s + Prime[n]; If[s == 2 || GCD @@ Transpose[ FactorInteger[s - 1]][[2]] > 1, Print[s - 1]], {n, 10^6}] (* _Robert G. Wilson v_, Oct 02 2005 *)
%Y A110997 Cf. A007504, A110979, A110996.
%Y A110997 Intersection of A001597 and A237589.
%K A110997 nonn,more
%O A110997 1,2
%A A110997 _Walter Kehowski_, Sep 30 2005
%E A110997 Initial 1 and a(9) added by _Jinyuan Wang_, Aug 10 2023