A089486 The second-smallest prime of the form (p-prime(n))/(prime(n)-1), where p is also prime.

5, 5, 3, 5, 3, 5, 11, 5, 3, 11, 7, 11, 29, 7, 5, 5, 5, 3, 5, 3, 7, 11, 137, 23, 7, 5, 3, 59, 11, 3, 5, 17, 47, 11, 11, 7, 7, 7, 5, 23, 11, 11, 3, 3, 29, 31, 11, 13, 29, 29, 17, 5, 19, 11, 29, 3, 11, 5, 5, 47, 5, 5, 11, 17, 3, 17, 3, 5, 11, 11, 5, 11, 41, 3, 19

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

For n = 1, prime(n) = 2, and the ratios generated are (3-2)/1 = 1 (not prime), (5-2)/1 = 3 (prime, first), (7-2)/1 = 5 (prime, second), and so a(1) = 5.

Mathematica

a[n_, r_] := Module[{p = Prime[n], q, rat, c = 0}, q = p; While[c < r, q = NextPrime[q]; If[PrimeQ[rat = (q - p)/(p - 1)], c++]]; rat]; Table[a[n, 2], {n, 1, 100}] (* Amiram Eldar, Jun 29 2024 *)

Prog

(PARI) /* r is the occurrence desired 1=first, 2=second etc. */ diff2sqp2(n, r) = { forprime(q=2, n, c=0; forprime(p=q+1, n, y=(p-q)/(q-1); if(y==floor(y), if(isprime(y), c++; if(c==r, print1(y", "); break)) ) ) ) }

Crossrefs

Cf. A089452, A089487.

Sequence in context: A308651 A260719 A291040 * A199617 A195693 A232813

Adjacent sequences: A089483 A089484 A089485 * A089487 A089488 A089489

Keyword

easy,nonn

Author

Cino Hilliard, Dec 28 2003

Extensions

Edited and corrected by D. S. McNeil, Dec 06 2010

More terms from Amiram Eldar, Jun 29 2024

Status

approved