A105405 Numbers k such that prime(k)-1 and prime(k+3)-1 have the same largest prime factor.

98, 156, 615, 1474, 2313, 66826, 82099, 150425, 188513, 274638, 321482, 523573, 874881, 6872507, 8101145, 22658038, 95011150, 159081273, 381064119, 509331868, 1216774420, 3067461737, 3356013378, 5447285266, 14949553319, 15007703651, 19495563000, 177439269404, 241783229062

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Mathematica

Do[p = Prime[n] - 1; q = Prime[n+3] - 1; l = Select[Divisors[p], PrimeQ]; m = Select[Divisors[q], PrimeQ]; If[Max[l] == Max[m], Print[n]], {n, 1, 10^7}] (* Ryan Propper, Sep 19 2005 *)

Prog

(PARI) \\prime indices such that gd of prime(x)+ k and prime(x+m) + k are equal
divpm1(n, m=3, k=-1) = { 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", ") ) ) }
\\Vector of the prime factors of n
ifactor(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

Sequence in context: A344843 A109553 A268253 * A341180 A044430 A044811

Adjacent sequences: A105402 A105403 A105404 * A105406 A105407 A105408

Keyword

nonn

Author

Cino Hilliard, May 01 2005

Extensions

More terms from Ryan Propper, Sep 19 2005

a(16)-a(27) from Donovan Johnson, Apr 03 2008

Name edited and offset changed by Jon E. Schoenfield, Nov 19 2018

a(28)-a(29) from Giovanni Resta, Nov 20 2018

Status

approved