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%I #48 Dec 23 2023 11:11:51
%S 2,6,8,12,16,20,22,26,34,36,40,58,64,68,78,82,84,86,98,112,120,126,
%T 142,146,148,152,156,160,168,188,190,194,196,208,216,218,222,238,240,
%U 244,246,254,264,272,282,286,294,300,302,306,308,316,320,330,338,344,348
%N Numbers m such that 3*m^2 + 1 is prime.
%C 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
%H Zak Seidov, <a href="/A111051/b111051.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = sqrt((A002648(n)-1)/3). - _Zak Seidov_, Feb 04 2016
%e 1 + 3*2^2 = 13 = A002648(1) is the 1st prime of this form, so a(1) = 2.
%e 1 + 3*6^2 = 109 = A002648(2) is the 2nd prime of this form, so a(2) = 6.
%e 1 + 3*8^2 = 193 = A002648(3) is the 3rd prime of this form, so a(3) = 8.
%e 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).
%p 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
%t Select[Range[400],PrimeQ[3#^2+1]&] (* _Harvey P. Dale_, Jul 17 2016 *)
%o (PARI) is(n)=isprime(3*n^2+1) \\ _Charles R Greathouse IV_, Feb 07 2017
%Y Cf. A002648, A121259.
%K nonn
%O 1,1
%A _Parthasarathy Nambi_, Oct 06 2005
%E More terms from _Jani Melik_, Jul 18 2007
%E Edited by _N. J. A. Sloane_, Sep 28 2007
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