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 A137691 #14 Sep 26 2024 04:10:24
%S A137691 1,2,3,4,5,6,10,11,12,13,14,18,38,376,377,378,379,380,381,382,383,384,
%T A137691 385,475,476,477,478,479,488,489,490,491,492,493,858,859,860,861,862,
%U A137691 863,864,2670,3261,3262,3263,3264,3265,4819,6034,6035,6036,6037,6038
%N A137691 Indices m such that A128646(m)+1 is prime, where A128646 = denominators of partial sums of 1/(prime(i)-1).
%C A137691 Terms corresponding to indices m = a(k) > 1000 are not certified primes but at least probable primes. Is there a simple explanation for the large gaps between a(k)=38 and a(k+1)=376; a(k)=864 and a(k+1)=2670, etc.?
%e A137691 n=3 is in this sequence because A128646(n)+1 = 5 is a prime (where A128646(3) is the denominator of 1/(2-1) + 1/(3-1) + 1/(5-1) = 7/4).
%o A137691 (PARI) print_A137691(i=0/*start checking at i+1*/)={my(s=sum(j=1,i,1/(prime(j)-1))); while(1, while(!ispseudoprime(1+denominator(s+=1/(prime(i++)-1))),);print1(i","))}
%Y A137691 Cf. A128646, A137689, A137690, A137692, A092063.
%K A137691 hard,nonn
%O A137691 1,2
%A A137691 _M. F. Hasler_, Feb 07 2008
%E A137691 Edited by _T. D. Noe_, Oct 30 2008