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A292084
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a(n) = least prime p such that 2*p + 1 equals (2*n - 1)*q where q is a prime, or 0 if no such p exists.
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2
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0, 7, 7, 17, 13, 71, 19, 37, 59, 47, 31, 149, 37, 67, 43, 263, 181, 227, 1091, 97, 61, 107, 67, 1433, 73, 127, 79, 137, 199, 383, 701, 157, 97, 167, 103, 461, 109, 487, 269, 197, 283, 2531, 127, 739, 311, 227, 139, 617, 2861, 643, 151, 257, 157, 1979, 163, 277
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OFFSET
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1,2
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COMMENTS
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Conjecture: 7 <= a(n) <= 4*n^2 - 5*n + 1 for n > 1. This conjecture implies that for every odd k > 1 there exist two primes p and q < 2*k such that k = (2*p + 1)/q.
Every positive term belongs to A053176.
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LINKS
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PROG
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(Magma) lst:=[]; for n in [2..56] do q:=1; repeat q+:=2; p:=Truncate((2*n*q-q-1)/2); until IsPrime(p) and IsPrime(q); Append(~lst, p); end for; [0] cat lst;
(PARI) a(n) = {if (n==1, return(0)); forprime(p=3, , q = (2*p+1)/(2*n-1); if ((denominator(q) == 1) && isprime(q), return (p)); ); } \\ Michel Marcus, Sep 16 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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