login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A235375 Integers k such that k^2 is of form y^2 + y + x^2 + x for positive y, x. 1
2, 6, 12, 20, 24, 30, 34, 36, 42, 52, 56, 66, 70, 72, 74, 88, 90, 96, 102, 108, 110, 126, 132, 138, 142, 156, 160, 162, 182, 186, 192, 196, 198, 204, 210, 214, 222, 228, 234, 236, 240, 264, 272, 294, 300, 306, 312, 318, 322, 324, 330, 342, 344, 354, 360, 366, 376, 380, 384, 394 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Integers k such that k^2 is the sum of two oblong numbers.

All terms are even. First k^2 that are expressible in m>1 ways:

m = 2, k = 12, {x,y} = {3,11},{8,8};

m = 3, k = 1168, {x,y} = {163,1156},{508,1051},{688,943};

m = 4, k = 600, {x,y} = {24,599},{135,584},{155,579},{260,540};

m = 5, k = 1746, {x,y} = {110,1742},{285,1722},{722,1589},{917,1485},{1062,1385};

m = 6, k = 6370, {x,y} = {1009,6289},{1330,6229},{2365,5914},{2665,5785},{3850,5074},{4105,4870}};

m = 8, k = 7332, {x,y} = {476,7316},{1083,7251},{1443,7188},{2036,7043},{3863,6231},{4368,5888},{4656,5663},{5111,5256}};

m = 9, k = 1734590;

m = 10, k = 1501632;

m = 12, k = 53766, {x,y} = {3537,53649},{6774,53337},{7625,53222},{8325,53117},{18317,50549},{19122,50250},{22125,49002},{22677,48749},{31077,43874},{32342,42950},{32825,42582},{35982,39950};

m = 13, k = 15994428;

m = 14, k = 36583944;

m = 16, k = 68906, {x,y} = {262,68905},{694,68902},{2242,68869},{14869,67282},{15802,67069},{16117,66994},{17305,66697},{26569,63577},{30430,61822},{30817,61630},{32194,60922},{33037,60469},{39877,56194},{43594,53362},{44782,52369},{45505,51742};

m = 18, k = 795918;

m = 20, k = 1501632;

m = 24, k = 338142;

m = 27, k = 216000900;

m = 32, k = 12464536;

m = 36, k = 6499622;

m = 40, k = 121608322;

m = 48, k = 10922046;

m = 64, k = 4210146;

m = 72, k = 207256338;

m = 96, k = 162026706;

Note that for k up 10^5 cases m = 7, 9, 10, 11, 13-15 are absent.

In general, odd values of m are much rarer than even values, why?

Case m = 7 is absent for k < 2*10^6. - Giovanni Resta, Jan 17 2014

Case m = 7 is absent for k <= 4*10^8. - Zak Seidov, Jan 26 2014

LINKS

Zak Seidov, Table of n, a(n) for n = 1..11196 All terms up to 10^5.

CROSSREFS

Cf. A000290 (squares), A002378 (oblong  numbers).

Sequence in context: A061078 A067114 A102711 * A141406 A045619 A028690

Adjacent sequences:  A235372 A235373 A235374 * A235376 A235377 A235378

KEYWORD

nonn

AUTHOR

Zak Seidov, Jan 17 2014

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 5 02:31 EDT 2022. Contains 355087 sequences. (Running on oeis4.)