|
| |
|
|
A154778
|
|
Numbers of the form a^2 + 5b^2 with positive integers a,b.
|
|
19
| |
|
|
6, 9, 14, 21, 24, 29, 30, 36, 41, 45, 46, 49, 54, 56, 61, 69, 70, 81, 84, 86, 89, 94, 96, 101, 105, 109, 116, 120, 126, 129, 134, 141, 144, 145, 149, 150, 161, 164, 166, 174, 180, 181, 184, 189, 196, 201, 205, 206, 214, 216, 224, 225, 229, 230, 241, 244, 245, 246
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Subsequence of A020669 (which allows for a=0 and/or b=0). See there for further references. See A155560 ff for intersection of sequences of type (a^2 + k b^2).
Also, subsequence of A000408 (with 5b^2 = b^2 + (2b)^2).
|
|
|
EXAMPLE
| a(1) = 6 = 1^2 + 5*1^2 is the least number that can be written as A+5B where A,B are positive squares.
a(2) = 9 = 2^2 + 5*1^2 is the second smallest number that can be written in this way.
|
|
|
MATHEMATICA
| formQ[n_] := Reduce[a > 0 && b > 0 && n == a^2 + 5 b^2, {a, b}, Integers] =!= False; Select[ Range[300], formQ] (* From Jean-François Alcover, Sep 20 2011 *)
Timing[mx = 300; limx = Sqrt[mx]; limy = Sqrt[mx/5]; Select[Union[Flatten[Table[x^2 + 5 y^2, {x, limx}, {y, limy}]]], # <= mx &]] (* T. D. Noe, Sep 20 2011 *)
|
|
|
PROG
| (PARI) isA154778(n, /* use optional 2nd arg to get other analogous sequences */c=5) = { for( b=1, sqrtint((n-1)\c), issquare(n-c*b^2) & return(1))}
for( n=1, 300, isA154778(n) & print1(n", "))
|
|
|
CROSSREFS
| Cf. A033205 (subsequence of primes). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 26 2009]
Sequence in context: A190461 A095098 A134859 * A106350 A020717 A196993
Adjacent sequences: A154775 A154776 A154777 * A154779 A154780 A154781
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| M. F. Hasler (www.univ-ag.fr/~mhasler), Jan 24 2009
|
| |
|
|
