

A154777


Numbers of the form x^2 + 2*y^2 with positive integers x and y.


35



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, 73, 75, 76, 81, 82, 83, 86, 88, 89, 96, 97, 99, 102, 107, 108, 113, 114, 118, 121, 123, 129, 131, 132, 134, 136, 137, 139, 144, 146, 147, 150, 152, 153, 162, 163
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OFFSET

1,1


COMMENTS

Subsequence of A002479 (which allows for x=0 and/or y=0). See there for further references. See A155560 ff for intersection of sequences of type (x^2 + k*y^2).
Also, subsequence of A000408 (with 2y^2 = y^2 + z^2).
If m and n are terms also x*m is (in particular any power of term is also a term).  Moshe Levin, Nov 30 2011
If m is a term also 2*m is.  Moshe Levin, 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.  Moshe Levin, Dec 01 2011


LINKS

Moshe Levin, 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[upto1]]}, 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((n1)\c), issquare(nc*b^2) & return(1))}
for( n=1, 200, isA154777(n) & print1(n", "))


CROSSREFS

Sequence in context: A201462 A189302 A086883 * A223731 A223732 A094740
Adjacent sequences: A154774 A154775 A154776 * A154778 A154779 A154780


KEYWORD

easy,nonn


AUTHOR

M. F. Hasler, Jan 24 2009


STATUS

approved



