A105406 Indices n of primes p(n), p(n+3) such that p(n)+1 and p(n+3)+1 have the same largest prime factor.

29, 53, 92, 126, 204, 281, 333, 489, 573, 816, 1169, 1585, 1885, 13906, 24059, 44421, 48142, 53394, 84043, 474045, 489910, 535841, 2135727, 3095936, 3925702, 4858924, 6618689, 8537111, 58246902, 163424560, 188474341, 193910248, 785107460, 847979055, 6040627719, 7900840637

Offset

2,1

Comments

No other term <=210000. - Emeric Deutsch, Feb 13 2006

Links

Table of n, a(n) for n=2..37.

Maple

with(numtheory): a:=proc(n) local a, b: a:=factorset(1+ithprime(n)): b:=factorset(1+ithprime(n+3)): if a[nops(a)]=b[nops(b)] then n else fi end: seq(a(n), n=1..10000); # it takes hours - Emeric Deutsch, Feb 13 2006

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

Sequence in context: A117328 A274227 A230027 * A124284 A054822 A034847

Adjacent sequences: A105403 A105404 A105405 * A105407 A105408 A105409

Keyword

nonn

Author

Cino Hilliard, May 01 2005

Extensions

One more term from Emeric Deutsch, Feb 13 2006

a(21)-a(37) from Donovan Johnson, Apr 03 2008

Status

approved