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.

User: Arashdeep Singh

Arashdeep Singh's wiki page.

Arashdeep Singh has authored 3 sequences.

A320772 Prime generating polynomial: a(n) = (4*n - 29)^2 + 58.

Original entry on oeis.org

683, 499, 347, 227, 139, 83, 59, 67, 107, 179, 283, 419, 587, 787, 1019, 1283, 1579, 1907, 2267, 2659, 3083, 3539, 4027, 4547, 5099, 5683, 6299, 6947, 7627, 8339, 9083, 9859, 10667, 11507, 12379, 13283, 14219, 15187, 16187, 17219, 18283, 19379, 20507, 21667, 22859, 24083, 25339, 26627, 27947
Offset: 1

Views

Author

Arashdeep Singh, Oct 21 2018

Keywords

Comments

The polynomial (4*n - 29)^2 + 58 generates 28 distinct primes in succession from n=1 to 28.

Links

Crossrefs

Cf. A048988.

Programs

  • Mathematica
    Array[(4# - 29)^2 + 58 &, 50] (* Amiram Eldar, Dec 15 2018 *)

Formula

From Elmo R. Oliveira, Feb 08 2025: (Start)
G.f.: x*(899*x^2 - 1550*x + 683)/(1-x)^3.
E.g.f.: exp(x)*(16*x^2 - 216*x + 899) - 899.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)

A318791 Prime generating polynomial: a(n) = 9*n^2 - 249*n + 1763.

Original entry on oeis.org

1523, 1301, 1097, 911, 743, 593, 461, 347, 251, 173, 113, 71, 47, 41, 53, 83, 131, 197, 281, 383, 503, 641, 797, 971, 1163, 1373, 1601, 1847, 2111, 2393, 2693, 3011, 3347, 3701, 4073, 4463, 4871, 5297, 5741, 6203, 6683, 7181, 7697, 8231, 8783, 9353
Offset: 1

Views

Author

Arashdeep Singh, Dec 15 2018

Keywords

Comments

This polynomial (9*n^2 - 249*n + 1763) generates 40 distinct primes in succession from n = 1 to 40.

Links

Crossrefs

Cf. A005846, A007635, A048059, A202018.

Programs

  • Maple
    seq(9*n^2-249*n+1763,n=1..50); # Muniru A Asiru, Dec 19 2018
  • Mathematica
    Array[9#^2 - 249# + 1763 &, 50] (* Amiram Eldar, Dec 15 2018 *)

Formula

From Chai Wah Wu, Feb 12 2019: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3.
G.f.: x*(-1763*x^2 + 3268*x - 1523)/(x - 1)^3. (End)
a(n) = p(41 - 3*n), where p(n) = n^2 + n + 41 is Euler's prime generating polynomial - see A202018 and A005846. - Peter Bala, Jun 10 2021
E.g.f.: exp(x)*(9*x^2 - 240*x + 1763) - 1763. - Elmo R. Oliveira, Feb 10 2025

A320752 Primes of the form 5*n^2 - 5*n + 13.

Original entry on oeis.org

13, 23, 43, 73, 113, 163, 223, 293, 373, 463, 563, 673, 1063, 1213, 1373, 1543, 1723, 1913, 2113, 2543, 3793, 4073, 4363, 4663, 4973, 5623, 6673, 7043, 8623, 9043, 9473, 12263, 12763, 14323, 15413, 15973, 17123, 17713, 18313, 19543, 20173, 22123, 23473, 26293
Offset: 1

Views

Author

Arashdeep Singh, Oct 20 2018

Keywords

Comments

The first 12 numbers of the form 5*n^2 - 5*n + 13 (n=1 to 12) are primes.

Links

Crossrefs

Cf. A090562.

Programs

  • GAP
    Filtered(List([1..75],n->5*n^2-5*n+13),IsPrime); # Muniru A Asiru, Oct 21 2018
  • Maple
    select(isprime,[seq(5*n^2-5*n+13,n=1..75)]); # Muniru A Asiru, Oct 21 2018
  • Mathematica
    Select[Table[5n^2-5n+13,{n,80}],PrimeQ] (* Harvey P. Dale, Aug 22 2021 *)
  • PARI
    terms(n) = my(i=0); for(k=1, oo, my(x=5*k^2-5*k+13); if(ispseudoprime(x), print1(x, ", "); i++); if(i==n, break))
/* Print initial 50 terms as follows */
terms(50) \\ Felix Fröhlich, Oct 20 2018

Extensions

More terms from Felix Fröhlich, Oct 20 2018

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