cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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

Views

Author

Alex Ratushnyak, Apr 25 2012

Keywords

Comments

Infinite under Bunyakovsky's conjecture. - Charles R Greathouse IV, Apr 25 2012

Crossrefs

Programs

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

Views

Author

Rajarshi Maiti, Oct 18 2017

Keywords

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

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.
		

Crossrefs

Union of A116581 and A100698.

Programs

  • 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
  • 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 *)
    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
Showing 1-2 of 2 results.