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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A187866 Greatest k such that prime(n)*(prime(n)-k)-1 and prime(n)*(prime(n)-k)+1 are twin primes, k >= 0 and k < prime(n) or -1 if no such k exists.

Original entry on oeis.org

0, 1, -1, 1, -1, -1, 11, 7, 17, 17, -1, -1, 11, 19, 41, -1, 41, -1, 43, 53, -1, -1, 29, 41, -1, 59, 97, 101, 61, 89, -1, 101, 131, 127, 137, 73, 133, 127, 137, 119, 47, 163, 101, 157, 131
Offset: 1

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Author

Pierre CAMI, Mar 14 2011

Keywords

Comments

Conjectures:
1. There are only 11 primes such that k does not exist: 5, 11, 13, 31, 37, 53, 61, 73, 79, 97, 127 (same as A183563).
2. There are only 20 primes such that k(n) = A187563(n): 2, 3, 7, 17, 19, 23, 41, 47, 59, 89, 103, 149, 167, 173, 179, 191, 277, 353, 433, 727.
3. If prime(n) >= 3 there are always at least 2 pairs of twin primes between prime(n) and prime(n)^2.

Links

Crossrefs

Cf. A187563.

Programs

  • Mathematica
    a[n_] := (k=Prime[n]-1; While[p = Prime[n]*(Prime[n]-k)-1; k>=0 && !(PrimeQ[p] && PrimeQ[p + 2]), k--]; k); a /@ Range[45] (* Jean-François Alcover, Mar 28 2011 *)
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