A137691 -id:A137691 - cp's OEIS frontend

A137692 Primes of the form A128646(k)+1 for some k (listed in A137691), where A128646 = denominators of partial sums of 1/(p(i)-1).

2, 3, 5, 11, 13, 61, 18481, 55441, 53413361, 11827018732969441

Offset: 1

M. F. Hasler, Feb 07 2008

nonn

The next term is A128646(376)+1, which has 226 decimal digits.

Cf. A128646, A137689, A137690, A137691, A092063.

A137691v = [1,2,3,4,5,6,10,11,12,13,14,18,38,376,377,378,379,380,381,382,383,384,385] /*see there*/; A137692 = vecsort(vector(15,k,A128646(A137691v[k])+1),8) /* ...,8 removes duplicate entries in PARI > 2.4.1 */

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

Original entry on oeis.org

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

M. F. Hasler, Feb 07 2008

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?

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

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","))}

Edited by T. D. Noe, Oct 30 2008

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

cp's OEIS Frontend

A137692 Primes of the form A128646(k)+1 for some k (listed in A137691), where A128646 = denominators of partial sums of 1/(p(i)-1).

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