Numbers n such that (prime(n)+composite(n))/n is an integer

1, 4, 346, 365, 891, 5668, 5677, 588138, 588142, 588144, 9872786, 9872948, 170160524, 441666155, 441666208

OFFSET

1

COMMENTS

The sequence also includes:

• A = {2992553599, 966501096569, 966501096596, 966501096597, 6696270270022}

where the corresponding primes (P) and composites (C) in A, are:

• P = {71670264959, 28957270703371, 28957270704179, 28957270704209, 214037416690099}

• C = {3143575016, 1004263290268, 1004263290297, 1004263290298, 6939502220627}

PROGRAMS

Perl

use 5.010;
use ntheory qw(:all);

my $p = 2;
my $k = 1;

local $| = 1;

forcomposites {

    if (($p + $_) % $k == 0) {
        print($k, ", ");
    }

    ++$k;
    $p = next_prime($p);
} 1e9;