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

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

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Last modified August 29 14:12 EDT 2014. Contains 246192 sequences.