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 A137689 #15 Sep 26 2024 22:19:25
%S A137689 3,4,5,7,8,9,10,11,15,16,23,24,26,47,48,54,78,79,80,243,244,245,246,
%T A137689 247,367,368,369,370,371,372,373,374,375,447,453,635,636,1656,1657,
%U A137689 1658,1659,1660,18618,18619,18620,18621,18622,18623,18624,18625,18626,18627,18628,18629,18630,18631,18632,18633,18634,18635
%N A137689 Indices m such that A128646(m)-1 is prime, where A128646 = denominator of partial sums of 1/(p(i)-1).
%C A137689 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)=80, a(k+1)=243 and a(k)=636, a(k+1)=1656?
%o A137689 (PARI) print_A137689(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 A137689 Cf. A128646, A137690, A137691, A137692, A092063.
%K A137689 hard,nonn
%O A137689 1,1
%A A137689 _M. F. Hasler_, Feb 07 2008
%E A137689 Edited by _T. D. Noe_, Oct 30 2008
%E A137689 a(43)-a(60) from _Jason Yuen_, Sep 26 2024