A137691 Indices m such that A128646(m)+1 is prime, where A128646 = denominators of partial sums of 1/(prime(i)-1).

1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 18, 38, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 475, 476, 477, 478, 479, 488, 489, 490, 491, 492, 493, 858, 859, 860, 861, 862, 863, 864, 2670, 3261, 3262, 3263, 3264, 3265, 4819, 6034, 6035, 6036, 6037, 6038

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)=38 and a(k+1)=376; a(k)=864 and a(k+1)=2670, etc.?

Examples

			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).
		

Crossrefs

Cf. A128646, A137689, A137690, A137692, A092063.

Programs

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","))}

Extensions

Edited by T. D. Noe, Oct 30 2008