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 A111051 Numbers m such that 3*m^2 + 1 is prime. 7
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 13 07:44 EDT 2024. Contains 375113 sequences. (Running on oeis4.)