A057605 -id:A057605 - cp's OEIS frontend

A175233 Numbers n with property that n and 4*n^2 + 163 are terms in A057605.

2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 16, 19, 24, 27, 28, 29, 33, 39, 45, 49, 58, 64, 69, 74, 80, 81, 82, 89, 97, 104, 110, 113, 114, 121, 127, 128, 132, 141, 150, 154, 160, 165, 169, 171, 180, 193, 197, 208, 212, 217, 220, 222, 227, 232, 233, 244, 253, 264, 269, 275

Offset: 1

Zak Seidov, Mar 09 2010

nonn

Numbers n with property that both m=4*n^2 + 163 and p=4*m^2 + 163 are primes.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Intersection of A057604 and A057605.

mpQ[n_]:=Module[{m=4n^2+163},And@@PrimeQ[{m,4m^2+163}]]; Select[Range[300], mpQ] (* Harvey P. Dale, Jul 15 2013 *)

n = 2: m = 4*n^2 + 163 = 179 and p = 4*m^2 + 163 = 128327 are primes.

Edited by Zak Seidov, Mar 17 2010

A059962 Duplicate of A057605.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 24, 25, 27, 28, 29

Offset: 1

dead

A057604 Primes of the form 4*k^2 + 163.

Original entry on oeis.org

163, 167, 179, 199, 227, 263, 307, 359, 419, 487, 563, 647, 739, 839, 947, 1063, 1187, 1319, 1459, 1607, 2099, 2467, 2663, 3079, 3299, 3527, 4007, 4259, 4519, 4787, 5347, 5639, 5939, 6247, 6563, 7219, 7559, 7907, 8263, 8627, 8999, 9767, 10163, 10567, 10979, 11399, 11827, 12263

Offset: 1

Tito Piezas III, Oct 08 2000

These numbers are not prime in O_Q(sqrt(-163)). If p = n^2 + 163, then (n - sqrt(-163))*(n + sqrt(-163)) = p. - Alonso del Arte, Dec 18 2017

Iain Fox, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)
S. A. Goudsmit, Unusual Prime Number Sequences, Nature Vol. 214 (1967), 1164.
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Cf. A005846, A007641, A007635, A057605.

[a: n in [0..400] | IsPrime(a) where a is 4*n^2 + 163] // Vincenzo Librandi, Aug 07 2010

Select[Table[4n^2 + 163, {n, 0, 70}], PrimeQ] (* Vincenzo Librandi, Jul 15 2012 *)

lista(nn) = for(n=0, nn, my(p = 4*n^2 + 163); if(isprime(p), print1(p, ", "))) \\ Iain Fox, Dec 19 2017

Sequence corrected by Vincenzo Librandi, Jul 15 2012

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A175233 Numbers n with property that n and 4*n^2 + 163 are terms in A057605.

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A059962 Duplicate of A057605.

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A057604 Primes of the form 4*k^2 + 163.

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