cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A292084 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.

Original entry on oeis.org

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
Offset: 1

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Author

Arkadiusz Wesolowski, Sep 08 2017

Keywords

Comments

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.

Crossrefs

Programs

  • 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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