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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
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
Sequence in context: A282345 A265765 A187563 * A166521 A187866 A206419
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.)