A105404 Indices n of primes p(n), p(n+2) such that p(n)+1 and p(n+2)+1 have the same largest prime factor.

1, 2, 3, 5, 7, 8, 22, 23, 259, 3598, 4808, 7715, 8821, 9155, 10765, 29745, 1776197, 2417850, 11568019, 1617124497, 5632000774

Offset

1,2

Comments

a(22) > 1.2*10^12, if it exists. - Giovanni Resta, May 14 2016

Links

Table of n, a(n) for n=1..21.

Example

The prime factors of prime(22)+1 = 2, 2, 2, 2, 5;
the prime factors of prime(24)+1 = 2, 3, 3, 5;
and 5 is the common largest prime factor.

Mathematica

t = {0, 3, 2}; Do[ t = {t[[2]], t[[3]], FactorInteger[Prime[n + 2] + 1][[ -1, 1]]}; If[t[[1]] == t[[3]], Print[n]], {n, 20000000}] (* Robert G. Wilson v, Jun 04 2005 *)

Prog

(PARI) /* prime indices such that gd of prime(x)+ k and prime(x+m) + k are equal */ divpm1(n, m, k) = { local(x, l1, l2, v1, v2); for(x=2, n, v1 = ifactor(prime(x)+ k); v2 = ifactor(prime(x+m)+k); l1 = length(v1); l2 = length(v2); if(v1[l1] == v2[l2], print1(x", ") ) ) }
ifactor(n) = /* Vector of the prime factors of n */ { local(f, j, k, flist); flist=[]; f=Vec(factor(n)); for(j=1, length(f[1]), for(k = 1, f[2][j], flist = concat(flist, f[1][j]) ); ); return(flist) }

Crossrefs

Cf. A105308.

Sequence in context: A352290 A350707 A285282 * A238378 A075012 A067090

Adjacent sequences: A105401 A105402 A105403 * A105405 A105406 A105407

Keyword

more,nonn

Author

Cino Hilliard, May 01 2005

Extensions

a(1), a(17)-(19) from Robert G. Wilson v, Jun 04 2005

a(20), a(21) from Donovan Johnson, Apr 03 2008

Status

approved