A155962 Numbers n with property that 3*(2n)^2+1 and 1*(2n)^2+3 are primes.
1, 4, 11, 32, 56, 73, 80, 109, 122, 143, 158, 175, 182, 217, 256, 262, 280, 284, 290, 308, 343, 347, 403, 431, 434, 437, 535, 581, 598, 619, 655, 665, 928, 973, 980, 1018, 1036, 1046, 1096, 1120, 1159, 1207, 1222, 1235, 1267, 1382, 1393, 1439, 1460, 1463, 1501
Offset: 1
Keywords
Examples
n=1, {3*(2n)^2+1, 1*(2n)^2+3}={13,7};
n=4, {3*(2n)^2+1, 1*(2n)^2+3}={193,67};
n=11, {3*(2n)^2+1, 1*(2n)^2+3}={1453,487};
n=32, {3*(2n)^2+1,1*(2n)^2+3}={12289,4099}.
Resulting primes are congruent to 1 mod 3.
Links
- Zak Seidov, Table of n,a (n) for n=1..1000
Programs
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Mathematica
Select[Range[1600],AllTrue[{3(2#)^2+1,(2#)^2+3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 30 2016 *)
Extensions
All the terms in the b-file had to be divided by 2. Corrected by N. J. A. Sloane, Aug 31 2009.
Comments