A282687 a(n) = strictly increasing number m, such that m+n is the next prime and m-n is the previous prime.

4, 5, 26, 93, 144, 157, 300, 1839, 1922, 3099, 3240, 4189, 5544, 5967, 6506, 10815, 11760, 12871, 30612, 33267, 35002, 36411, 81486, 86653, 95676, 103263, 106060, 153219, 181332, 189097, 190440, 288615, 294596, 326403, 399318, 507253, 515004, 570291, 642320

Offset

1,1

Links

Daniel Suteu, Table of n, a(n) for n = 1..100

Example

For n = 5, a(5) = 144, because the next prime after 144 is 149 and the previous prime before 144 is 139, where both have an equal distance of 5 from 144.

Mathematica

a = {}; Do[If[n == 1, k = 1, k = Max@ a + 1]; While[Nand[k - n == NextPrime[k, -1], k + n == NextPrime@ k], k++]; AppendTo[a, k], {n, 41}]; a (* Michael De Vlieger, Feb 20 2017 *)

Prog

(Perl)
use ntheory qw(:all);
for (my ($n, $k) = (1, 1) ; ; ++$n) {
    my $p = prev_prime($n) || next;
    my $q = next_prime($n);
    if ($n-$p == $k and $q-$n == $k) {
        printf("%s %s\n", $k++, $n);
    }
}

Crossrefs

Cf. A087378, A087711, A282690.

Sequence in context: A084465 A056200 A282690 * A153429 A270217 A270274

Adjacent sequences: A282684 A282685 A282686 * A282688 A282689 A282690

Keyword

nonn

Author

Daniel Suteu, Feb 20 2017

Status

approved