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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 (list; graph; refs; listen; history; text; internal format)
 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), (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 PROG (PARI) r is the occurrence desired 1=first, 2=second etc. diff2sqp2(n, r) = { forprime(q=3, 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 STATUS approved

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