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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
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
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
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