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
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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
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Maple
select(isprime, [seq(seq((k-1)*k*(k+1)+q,q=[-1,1]),k=1..100)]); # Robert Israel, Jan 04 2018
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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 *) Select[Flatten[Table[k^3-k+{-1,1},{k,60}]],PrimeQ] (* Harvey P. Dale, May 19 2025 *) -
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
Extensions
Corrected and extended by Robert G. Wilson v, Oct 18 2017
Comments