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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: Charles Delaporte

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Charles Delaporte has authored 1 sequences.

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

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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 *)

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