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 A089487 The third-smallest prime of the form (p-prime(n))/(prime(n)-1), where p is also prime. 2
 11, 7, 17, 11, 5, 7, 41, 23, 17, 23, 13, 31, 53, 17, 17, 17, 29, 19, 19, 5, 13, 13, 149, 41, 11, 11, 5, 137, 19, 5, 7, 23, 59, 13, 29, 11, 11, 13, 11, 59, 23, 13, 11, 5, 41, 41, 19, 19, 71, 31, 23, 11, 31, 41, 41, 47, 41, 7, 11, 53, 17, 29, 19, 53, 5, 101, 13 (list; graph; refs; listen; history; text; internal format)
 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), (11-2)/1 = 9 (not prime) and (13-2)/1 = 11 (prime, third and selected a(1)). MAPLE A089487 := proc(n) local ct, q, p ; ct := 0 ; q := ithprime(n) ; p := nextprime(q) ; while true do while true do if type( (p-q)/(q-1), 'integer') then if isprime( (p-q)/(q-1)) then break; end if; end if; p := nextprime(p) ; end do: ct := ct+1 ; if ct = 3 then return (p-q)/(q-1); end if; p := nextprime(p) ; end do: end proc: seq(A089487(n), n=1..44) ; # R. J. Mathar, Dec 06 2010 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, 3], {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, A089486. Sequence in context: A282345 A265765 A187563 * A166521 A187866 A206419 Adjacent sequences: A089484 A089485 A089486 * A089488 A089489 A089490 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

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Last modified July 21 00:10 EDT 2024. Contains 374461 sequences. (Running on oeis4.)