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A092063
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Numbers k such that numerator of Sum_{i=1..k} 1/(prime(i)-1) is prime.
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6
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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1/(2-1) + 1/(3-1) = 3/2 and 3 is prime so a(1)=2.
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MATHEMATICA
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Position[Accumulate[1/(Prime[Range[3100]]-1)], _?(PrimeQ[ Numerator[ #]]&)]//Flatten (* Harvey P. Dale, Oct 16 2016 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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hard,nonn,changed
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AUTHOR
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Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Feb 20 2004
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EXTENSIONS
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STATUS
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approved
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