A155716 Numbers of the form N = a^2 + 6b^2 for some positive integers a,b.

7, 10, 15, 22, 25, 28, 31, 33, 40, 42, 49, 55, 58, 60, 63, 70, 73, 79, 87, 88, 90, 97, 100, 103, 105, 106, 112, 118, 121, 124, 127, 132, 135, 145, 150, 151, 154, 159, 160, 166, 168, 175, 177, 186, 193, 196, 198, 199, 202, 214, 217, 220, 223, 225, 231, 232, 240

Offset: 1

Author

M. F. Hasler, Jan 25 2009

Keywords

• easy
• nonn

Comments

Subsequence of A002481 (which allows for a and b to be zero).

Primes are in A033199. - Bernard Schott, Sep 20 2019

Links

• David A. Corneth, Table of n, a(n) for n = 1..17743 (terms <= 10^5)

Crossrefs

Cf. A002481, A033199.

Cf. A000404, A154777, A092572, A097268, A154778, A155707-A155717, A155560-A155578.

Programs

Mathematica

With[{upto=240},Select[Union[#[[1]]^2+6#[[2]]^2&/@Tuples[ Range[Sqrt[ upto]], 2]],#<=upto&]] (* Harvey P. Dale, Aug 05 2016 *)

PARI

isA155716(n,/* optional 2nd arg allows us to get other sequences */c=6) = { for(b=1,sqrtint((n-1)\c), issquare(n-c*b^2) & return(1))}
for( n=1,999, isA155716(n) & print1(n","))

PARI

upto(n) = my(res=List()); for(i=1,sqrtint(n),for(j=1, sqrtint((n - i^2) \ 6), listput(res, i^2 + 6*j^2))); listsort(res,1); res \\ David A. Corneth, Sep 18 2019