

A024352


Numbers which are the difference of two positive squares, c^2  b^2 with 1 <= b < c.


20



3, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 91, 92, 93
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OFFSET

1,1


COMMENTS

These are the solutions to the equation x^2 + xy = n where y mod 2 is zero, y is positive and x is any positive integer.  Andrew Plewe, Oct 19 2007
Ordered different terms of A120070 = 3, 8, 5, 15, 12, 7, ... (which contains two 15's, two 40's, and two 48's). Complement: A139544. (See A139491.)  Paul Curtz, Sep 01 2009
A024359(a(n)) > 0.  Reinhard Zumkeller, Nov 09 2012
If a(n) mod 6 = 3, n>1, then a(n) = c^2f(a(n))^2 where f(n) = (floor(4*n/3)3n)/2. For example, 171 = 30^227^2 and f(171) = 27.  Gary Detlefs, Jul 15 2014


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
Ron Knott, Pythagorean Triples and Online Calculators
Index entries for linear recurrences with constant coefficients, signature (1,0,1,1).


FORMULA

Consists of all positive integers except 1, 4 and numbers == 2 mod 4.
a(n) = a(n3) + 4, n>4.
G.f.: (x^4  2*x^3 + 2*x^2 + 2*x + 3)/(x^4  x^3  x + 1).  Ralf Stephan, before May 13 2008
a(n) = a(n1)+a(n3)a(n4), for n>5.  Ant King, Oct 03 2011
a(n) = 4 + floor((4*n3)/3), n>1.  Gary Detlefs, Jul 15 2014


MATHEMATICA

Union[ Flatten[ Table[ Select[ Table[b^2  c^2, {c, b  1}], # < 100 &], {b, 100}]]] (* Robert G. Wilson v, Jun 05 2004 *)


PROG

(Haskell)
a024352 n = a024352_list !! (n1)
a024352_list = 3 : drop 4 a042965_list
 Reinhard Zumkeller, Nov 09 2012
(PARI) is(n)=(n%4!=2 && n>4)  n==3 \\ Charles R Greathouse IV, May 31 2013


CROSSREFS

Same as A042965 except for initial terms.  Michael Somos, Jun 08 2000
Different from A020884.
Cf. A009005, A020884.
Sequence in context: A025051 A020884 A183855 * A288525 A134407 A218979
Adjacent sequences: A024349 A024350 A024351 * A024353 A024354 A024355


KEYWORD

nonn,easy


AUTHOR

David W. Wilson


EXTENSIONS

Edited by N. J. A. Sloane, Sep 19 2008


STATUS

approved



