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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A371349 Odd addends k > 0 such that x^2 + x + k produces a new minimum of its Hardy-Littlewood Constant.

Original entry on oeis.org

1, 3, 9, 15, 33, 63, 75, 225, 243, 273, 453, 813, 1275, 1443, 2763, 3003, 6693, 9933, 10515
Offset: 1

Views

Author

Hugo Pfoertner, Apr 11 2024, suggested by Martin Raab

Keywords

Links

Crossrefs

Cf. A331940 for more information.

Programs

  • PARI
    \\ Uses function HardyLittlewood2 from a221712.gp; see link in A331940
a371349(upto) = {my (Hmin=oo); forstep (k=1, upto, 2, my (H=HardyLittlewood2(x^2+x+k)); if (H

A356727 Primes of the form 4*k^2 + 84*k + 43.

Original entry on oeis.org

43, 131, 227, 331, 443, 563, 691, 827, 971, 1123, 1283, 1451, 1627, 1811, 2003, 2203, 2411, 2851, 3083, 3323, 3571, 4091, 4363, 4643, 4931, 5227, 5531, 5843, 6163, 6491, 6827, 7523, 7883, 8627, 9011, 9403, 9803, 10211, 10627, 11483, 11923, 13291, 13763, 14243, 14731, 15227, 15731
Offset: 1

Views

Author

Charles Delaporte, Aug 24 2022

Keywords

Comments

The polynomial 4*k^2 + 84*k + 43 has prime values for k from 0 to 16. The proportion of prime numbers (23.28%) obtained among the first ten million values is slightly higher than that (22.08%) obtained with Euler's polynomial k^2 - k + 41.
The polynomial 4*k^2 + 84*k + 43 produces a Hardy-Littlewood constant of 7.3291180993696....

Links

Crossrefs

Cf. A005846, A221712, A331940.

Programs

  • Mathematica
    Select[Table[4k^2+84k+43,{k,0,60}],PrimeQ] (* Harvey P. Dale, May 07 2023 *)
Previous Showing 11-12 of 12 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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