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A089486
The second-smallest prime of the form (p-prime(n))/(prime(n)-1), where p is also prime.
2
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
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
Sequence in context: A308651 A260719 A291040 * A199617 A195693 A232813
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