A137689 Indices m such that A128646(m)-1 is prime, where A128646 = denominator of partial sums of 1/(p(i)-1).

3, 4, 5, 7, 8, 9, 10, 11, 15, 16, 23, 24, 26, 47, 48, 54, 78, 79, 80, 243, 244, 245, 246, 247, 367, 368, 369, 370, 371, 372, 373, 374, 375, 447, 453, 635, 636, 1656, 1657, 1658, 1659, 1660, 18618, 18619, 18620, 18621, 18622, 18623, 18624, 18625, 18626, 18627, 18628, 18629, 18630, 18631, 18632, 18633, 18634, 18635

Offset: 1

Author

M. F. Hasler, Feb 07 2008

Keywords

• hard
• nonn

Comments

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?

Crossrefs

Cf. A128646, A137690, A137691, A137692, A092063.

Programs

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","))}

Extensions

Edited by T. D. Noe, Oct 30 2008

a(43)-a(60) from Jason Yuen, Sep 26 2024