A089487 The third-smallest prime of the form (p-prime(n))/(prime(n)-1), where p is also prime.

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

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