

A154777


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


37



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 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[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

Cf. A000408, A002479, A155560, A338432 (triangle version of array), A339047 (multiplicities).
Sequence in context: A201462 A189302 A086883 * A338432 A288821 A343306
Adjacent sequences: A154774 A154775 A154776 * A154778 A154779 A154780


KEYWORD

easy,nonn


AUTHOR

M. F. Hasler, Jan 24 2009


STATUS

approved



