A391974 - OEIS

A391974

Numbers k such that (k*(k+1)*(k+2)*(k+3) + k + (k+1) + (k+2) + (k+3))/2 and (k*(k+1)*(k+2)*(k+3) - k - (k+1) - (k+2) - (k+3))/2 are both prime.

1, 2, 4, 5, 11, 20, 40, 46, 56, 65, 68, 107, 130, 133, 140, 145, 221, 287, 314, 362, 418, 436, 446, 475, 481, 517, 536, 593, 595, 779, 788, 809, 1057, 1061, 1063, 1103, 1195, 1285, 1292, 1334, 1337, 1370, 1474, 1510, 1547, 1636, 1649, 1736, 1831, 1838, 1918, 1936, 1993, 2021, 2324, 2482, 2491

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Numbers k such that (k^4 + 6*k^3 + 11*k^2 + 10*k + 6)/2 and (k^4 + 6*k^3 + 11*k^2 + 2*k - 6)/2 are prime.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(3) = 4 is a term because (4*5*6*7 + 4 + 5 + 6 + 7)/2 = 431 and (4*5*6*7 - 4 - 5 - 6 - 7)/2 = 409 are prime.

MAPLE

filter:= n -> isprime((n^4 + 6*n^3 + 11*n^2 + 10*n + 6)/2) and isprime((n^4 + 6*n^3 + 11*n^2 + 2*n - 6)/2):

select(filter, [$1..10000]);

MATHEMATICA

q[k_]:=PrimeQ[(k^4 + 6*k^3 + 11*k^2 + 10*k + 6)/2]&&PrimeQ[(k^4 + 6*k^3 + 11*k^2 + 2*k- 6)/2]; Select[Range[2500], q] (* James C. McMahon, Feb 14 2026 *)

CROSSREFS

Cf. A136014.

Sequence in context: A049913 A223220 A113058 * A066145 A095022 A279050

Adjacent sequences: A391971 A391972 A391973 * A391975 A391976 A391977

KEYWORD

nonn

AUTHOR

Will Gosnell and Robert Israel, Feb 09 2026

STATUS

approved