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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A221903 Primes of the form 2*n^2 + 42*n + 19.

Original entry on oeis.org

163, 811, 1423, 1783, 2179, 3079, 3583, 9739, 11503, 13411, 14419, 17659, 22483, 25111, 26479, 27883, 42139, 49411, 55243, 57259, 70111, 72379, 77023, 79399, 86743, 97039, 116443, 119359, 125299, 140779, 181603, 188911, 207811
Offset: 1

Views

Author

Vincenzo Librandi, Feb 01 2013

Keywords

Comments

Conjecture: 2^a(n)-1 is not prime; in other words, these primes are included in A054723.
2*a(n) + 403 is a square. - Vincenzo Librandi, Apr 10 2015

Crossrefs

Cf. Primes of the form 2*n^2+2*(2*k+3)*n+(2*k+1): A176549 (k=0), A154577 (k=2), A154592 (k=3), A154601 (k=4), A217494 (k=7), this sequence (k=9), A217495 (k=10), A217496 (k=11), A217497 (k=12), A217498 (k=13), A217499 (k=16), A217500 (k=17), A217501 (k=18), A217620 (k=19), A217621 (k=21).
Cf. A054723.

Programs

  • Magma
    [a: n in [1..500] | IsPrime(a) where a is 2*n^2 + 42*n + 19];
  • Mathematica
    Select[Table[2 n^2 + 42 n + 19, {n, 500}], PrimeQ]

A176545 Numbers k>0 such that 2*k^2+14*k+5 is prime.

Original entry on oeis.org

2, 9, 11, 12, 14, 17, 21, 24, 26, 39, 44, 47, 59, 77, 86, 87, 89, 101, 116, 117, 122, 126, 131, 137, 147, 152, 161, 164, 177, 179, 189, 191, 192, 201, 212, 219, 222, 231, 249, 257, 261, 264, 284, 287, 296, 306, 317, 326, 329, 336, 347, 369, 387, 389, 411, 417
Offset: 1

Views

Author

Vincenzo Librandi, Apr 20 2010

Keywords

Comments

Conjecture: If p = 2*k^2 + 14*k + 5 then 2^p - 1 is not prime.

Crossrefs

Cf. A154577 (Primes of the form 2n^2 + 14n + 5), A144562(Triangle read by rows where T(m, n) = 2m*n + m + n - 1).

Programs

  • Magma
    [n: n in [1..1000]| IsPrime(2*n^2+14*n+5)];
  • Mathematica
    Select[Range[500], PrimeQ[2#^2 + 14# + 5] &] (* Harvey P. Dale, Jan 09 2011 *)
Previous Showing 11-12 of 12 results.