A182332
Primes of the form n^3 + n - 1.
Original entry on oeis.org
29, 67, 349, 1009, 3389, 4111, 5849, 9281, 15649, 19709, 35969, 46691, 59357, 79549, 97381, 132701, 140659, 166429, 250109, 389089, 474629, 531521, 658589, 804449, 830677, 884831, 1000099, 1092829, 1157729, 1295137, 1405039, 1520989, 1601729, 1728119, 1906747
Offset: 1
A293861
Primes of the form (k - 1) * k * (k + 1) +- 1, k >= 1.
Original entry on oeis.org
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*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.
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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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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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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 *)
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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
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