A111051 Numbers m such that 3*m^2 + 1 is prime.

2, 6, 8, 12, 16, 20, 22, 26, 34, 36, 40, 58, 64, 68, 78, 82, 84, 86, 98, 112, 120, 126, 142, 146, 148, 152, 156, 160, 168, 188, 190, 194, 196, 208, 216, 218, 222, 238, 240, 244, 246, 254, 264, 272, 282, 286, 294, 300, 302, 306, 308, 316, 320, 330, 338, 344, 348

Offset

1,1

Comments

The resulting primes are the generalized cuban primes of the form (x^3-y^3)/(x-y), x=y+2 (see A002648). - Jani Melik, Jul 18 2007

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Formula

a(n) = sqrt((A002648(n)-1)/3). - Zak Seidov, Feb 04 2016

Example

1 + 3*2^2 = 13 = A002648(1) is the 1st prime of this form, so a(1) = 2.
1 + 3*6^2 = 109 = A002648(2) is the 2nd prime of this form, so a(2) = 6.
1 + 3*8^2 = 193 = A002648(3) is the 3rd prime of this form, so a(3) = 8.
If m=98 then 3*m^2 + 1 = 28813 = A002648(19) is prime (the 19th of this form), so 98 is a term (the 19th).

Maple

ts_kubpra_ind:=proc(n) local i, tren, ans; ans:=[ ]: for i from 0 to n do tren:=1+3*i^2: if (isprime(tren)='true') then ans:=[ op(ans), i ] fi od: RETURN(ans); end: ts_kubpra_ind(2000); # Jani Melik, Jul 18 2007

Mathematica

Select[Range[400], PrimeQ[3#^2+1]&] (* Harvey P. Dale, Jul 17 2016 *)

Prog

(PARI) is(n)=isprime(3*n^2+1) \\ Charles R Greathouse IV, Feb 07 2017

Crossrefs

Cf. A002648, A121259.

Sequence in context: A283233 A189400 A285342 * A077561 A008407 A111224

Adjacent sequences: A111048 A111049 A111050 * A111052 A111053 A111054

Keyword

nonn

Author

Parthasarathy Nambi, Oct 06 2005

Extensions

More terms from Jani Melik, Jul 18 2007

Edited by N. J. A. Sloane, Sep 28 2007

Status

approved