login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007970 Rhombic numbers. 10
3, 7, 8, 11, 15, 19, 23, 24, 27, 31, 32, 35, 40, 43, 47, 48, 51, 59, 63, 67, 71, 75, 79, 80, 83, 87, 88, 91, 96, 99, 103, 104, 107, 115, 119, 120, 123, 127, 128, 131, 135, 136, 139, 143, 151, 152, 159, 160, 163, 167, 168, 171, 175, 176, 179 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A000037; A007968(a(n))=2; A002145 is a subsequence;

A191856(n) = A007966(a(n)); A191857(n) = A007967(a(n));

a(n) = A191856(n)*A191857(n). [Reinhard Zumkeller, Jun 18 2011]

LINKS

Table of n, a(n) for n=1..55.

J. H. Conway, On Happy Factorizations, J. Integer Sequences, Vol. 1, 1998, #1.

MATHEMATICA

r[b_, c_] := (red = Reduce[x > 0 && y > 0 && b*x^2 + 2 == c*y^2, {x, y}, Integers] /. C[1] -> 1 // Simplify; If[Head[red] === Or, First[red], red]); f[n_] := f[n] = If[! IntegerQ[Sqrt[n]], Catch[Do[{b, c} = bc; If[ (r0 = r[b, c]) =!= False, {x0, y0} = {x, y} /. ToRules[r0]; If[OddQ[x0] && OddQ[y0], Throw[n]]]; If[ (r0 = r[c, b]) =!= False, {x0, y0} = {x, y} /. ToRules[r0]; If[OddQ[x0] && OddQ[y0], Throw[n]]], {bc, Union[Sort[{#, n/#}] & /@ Divisors[n]]} ]]]; A007970 = Reap[ Table[ If[f[n] =!= Null, Print[f[n]]; Sow[f[n]]], {n, 1, 180}] ][[2, 1]](* Jean-François Alcover, Jun 26 2012 *)

CROSSREFS

Every number belongs to exactly one of A000290, A007969, A007970.

Sequence in context: A078466 A047528 A069122 * A134258 A028972 A153030

Adjacent sequences:  A007967 A007968 A007969 * A007971 A007972 A007973

KEYWORD

nonn

AUTHOR

J. H. Conway

EXTENSIONS

159 and 175 inserted by Jean-François Alcover, Jun 26 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 17 18:04 EST 2014. Contains 252034 sequences.