OFFSET
1,1
COMMENTS
Subsequence of A002479 (which allows for x=0 and/or y=0). See there for further references. See A155560 cf for intersection of sequences of type (x^2 + k*y^2).
Also, subsequence of A000408 (with 2*y^2 = y^2 + z^2).
If m and n are terms also n*m is (in particular any power of term is also a term). - Zak Seidov, Nov 30 2011
If m is a term, 2*m is also. - Zak Seidov, Nov 30 2011
Select terms that are multiples of 25: 75, 150, 225, 275, 300, 425, 450, 475, 550, 600, 675, 825, 850, 900, 950, 1025, 1075, 1100, ... Divide them by 25: 3, 6, 9, 11, 12, 17, 18, 19, 22, 24, 27, 33, 34, 36, 38, 41, 43, 44, 48, 51, 54, 57, 59, 66, 67, 68, 72, ... and we get the original sequence. - Zak Seidov, Dec 01 2011
This sequence is closed under multiplication because A002479 is. - Jerzy R Borysowicz, Jun 13 2020
LINKS
Zak Seidov, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1) = 3 = 1^2 + 2*1^2 is the least number that can be written as A + 2B where A, B are positive squares.
a(2) = 6 = 2^2 + 2*1^2 is the second smallest number that can be written in this way.
MATHEMATICA
f[upto_]:=Module[{max=Ceiling[Sqrt[upto-1]]}, Select[Union[ First[#]^2+ 2Last[#]^2&/@Tuples[Range[13], {2}]], #<=upto&]]; f[200] (* Harvey P. Dale, Jun 17 2011 *)
PROG
(PARI) isA154777(n, /* use optional 2nd arg to get other analogous sequences */c=2) = { for( b=1, sqrtint((n-1)\c), issquare(n-c*b^2) & return(1))}
for( n=1, 200, isA154777(n) & print1(n", "))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
M. F. Hasler, Jan 24 2009
STATUS
approved