A199365 -id:A199365

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A115104

Numbers n such that 4*n^3 + 1 is prime.

+10
8

1, 3, 4, 7, 9, 10, 19, 25, 34, 37, 39, 42, 49, 54, 55, 72, 73, 78, 85, 87, 93, 94, 102, 108, 109, 118, 138, 142, 147, 157, 160, 165, 168, 175, 192, 195, 202, 210, 214, 220, 228, 232, 243, 247, 249, 250, 252, 253, 258, 267, 273, 274, 279, 289, 297

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

For any n in this sequence, 3*(4*n^3 + 1) has the same nonzero digits as its prime factors in base 2n. - Ely Golden, Dec 12 2016

LINKS

Ely Golden, Table of n, a(n) for n = 1..1000

EXAMPLE

If n=94 then (4*n^3 + 1) = 3322337 (prime).

MATHEMATICA

Select[Range[300], PrimeQ[4*#^3 + 1] &] (* Stefan Steinerberger, Mar 04 2006 *)

PROG

(PARI) is(n)=isprime(4*n^3+1) \\ Charles R Greathouse IV, Feb 17 2017

CROSSREFS

Cf. A001912. See A199307 for the actual primes.

See also A199364, A199365, A199366, A199367, A199368, A199369.

KEYWORD

nonn

AUTHOR

Parthasarathy Nambi, Mar 02 2006

EXTENSIONS

More terms from Stefan Steinerberger, Mar 04 2006

STATUS

approved

A199364

Numbers k such that 4k^3 + 3 is prime.

+10
3

0, 1, 5, 10, 14, 20, 28, 34, 38, 49, 55, 59, 61, 80, 98, 103, 118, 133, 145, 146, 154, 160, 185, 196, 206, 224, 229, 241, 245, 250, 251, 320, 325, 334, 376, 383, 385, 388, 398, 416, 418, 440, 451, 454, 475, 476, 481, 488, 490, 493, 496, 500

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

See comment in A199307.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

MATHEMATICA

Select[Range[0, 3000], PrimeQ[4#^3+3]&] (* Vincenzo Librandi, Aug 01 2012 *)

PROG

(Magma) [n: n in [0..500] | IsPrime(4*n^3+3)]; // Bruno Berselli, Nov 08 2011

(PARI) is(n)=isprime(4*n^3+3) \\ Charles R Greathouse IV, May 22 2017

CROSSREFS

Cf. A199307, A199365.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 05 2011

EXTENSIONS

First term added by Vincenzo Librandi, Nov 08 2011

STATUS

approved

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