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A092063
Numbers k such that numerator of Sum_{i=1..k} 1/(prime(i)-1) is prime.
6
2, 3, 4, 7, 8, 15, 19, 21, 22, 25, 26, 31, 34, 45, 46, 52, 65, 69, 79, 85, 89, 98, 102, 122, 137, 149, 181, 195, 210, 220, 316, 325, 340, 385, 436, 466, 497, 934, 972, 1180, 1211, 1212, 1639, 1807, 2075, 2104, 3100, 3258, 3563, 3688, 4528, 4760, 4934, 6151, 6185, 7579, 8625, 8694, 9205
OFFSET
1,1
COMMENTS
Note that the definition here is subtly different from that of A092065.
Terms a(k) < 1000 correspond to primes. Beyond, numerators are probable primes. Note that A120271(3100) has 2187 digits. - M. F. Hasler, Feb 06 2008
Intersection of A000040 (the primes) and A120271 (numerators of partial sums of 1/(prime(i)-1)). - M. F. Hasler, Feb 06 2008
a(60) > 10000. - Jason Yuen, Aug 26 2024
EXAMPLE
1/(2-1) + 1/(3-1) = 3/2 and 3 is prime so a(1)=2.
MATHEMATICA
Position[Accumulate[1/(Prime[Range[3100]]-1)], _?(PrimeQ[ Numerator[ #]]&)]//Flatten (* Harvey P. Dale, Oct 16 2016 *)
PROG
(PARI) A120271(n) = numerator(sum(k=1, n, 1/(prime(k)-1)));
for (i=1, 500, if(isprime(A120271(i)), print1(i, ", ")));
(PARI) print_A092063( i=0 /* start testing at i+1 */)={local(s=sum(j=1, i, 1/(prime(j)-1))); while(1, while(!ispseudoprime(numerator(s+=1/(prime(i++)-1))), ); print1(i", "))} \\ M. F. Hasler, Feb 06 2008
CROSSREFS
Sequence in context: A116961 A300486 A120611 * A227007 A370858 A126850
KEYWORD
hard,nonn
AUTHOR
Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Feb 20 2004
EXTENSIONS
More terms from M. F. Hasler, Feb 06 2008
Edited by T. D. Noe, Oct 30 2008
Corrected by Harvey P. Dale, Oct 16 2016
a(48)-a(59) from Jason Yuen, Aug 26 2024
STATUS
approved