A293861 Primes of the form (k - 1) * k * (k + 1) +- 1, k >= 1.

5, 7, 23, 59, 61, 211, 337, 503, 719, 991, 1319, 1321, 2729, 2731, 3359, 3361, 4079, 5813, 6841, 9239, 9241, 10627, 12143, 13799, 15601, 17551, 24359, 29759, 29761, 42839, 42841, 46619, 54833, 59281, 68879, 68881, 74047, 91079, 91081, 110543, 124951, 140557

Offset

1,1

Comments

Number of terms less than 10^k, k=1,2,3,...: 2, 5, 10, 21, 39, 66, 118, 213, 419, 770, 1486, 2886, 5575, 11096, 22338, 44710, 89992, 182554, 370614, 754201, 1541613, 3159885, ... - Muniru A Asiru, Jan 29 2018

Links

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

Example

1*2*3 = 6; 6-1 = 5, a prime, so it is a term; 6+1 = 7, a prime, so it is a term;
2*3*4 = 24; 24-1 = 23, a prime so is a term, 24+1 = 25, not a prime and so not a term;
100*101*102 = 1030200; 1030200+1 = 1030201 is a term.

Maple

select(isprime, [seq(seq((k-1)*k*(k+1)+q, q=[-1, 1]), k=1..100)]); # Robert Israel, Jan 04 2018

Mathematica

lst = {}; k = 1; While[k < 61, p = k^3 - k; If[ PrimeQ[p -1], AppendTo[lst, p -1]]; If[PrimeQ[p +1], AppendTo[lst, p +1]]; k++]; lst (* Robert G. Wilson v, Oct 18 2017 *)

Prog

(PARI) lista(nn) = {for (n=1, nn, if (isprime(p=n*(n+1)*(n+2)-1), print1(p, ", ")); if (isprime(p=n*(n+1)*(n+2)+1), print1(p, ", ")); ); } \\ Michel Marcus, Oct 19 2017
(GAP) Filtered(Set(Flat(List([1..60], k -> List([1, -1], q -> (k-1)*k*(k+1)+q)))), IsPrime); # Muniru A Asiru, Jan 29 2018

Crossrefs

Union of A116581 and A100698.

Sequence in context: A121182 A173970 A028287 * A321462 A121605 A226657

Adjacent sequences: A293858 A293859 A293860 * A293862 A293863 A293864

Keyword

nonn,easy

Author

Rajarshi Maiti, Oct 18 2017

Extensions

Corrected and extended by Robert G. Wilson v, Oct 18 2017

Status

approved