A155716 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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)

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A002481, A033199.

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

Sequence in context: A154681 A225676 A030764 * A025002 A120136 A020743

Adjacent sequences: A155713 A155714 A155715 * A155717 A155718 A155719

KEYWORD

easy,nonn

AUTHOR

M. F. Hasler, Jan 25 2009

STATUS

approved