A139544 Numbers which are not the difference of two squares of positive integers.

1, 2, 4, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202, 206, 210, 214, 218, 222, 226, 230

Offset

1,2

Comments

Conjecture: these numbers do not occur in A139491.

Complement sequence to A024352.

All odd numbers 2k+1 for k>0 can be represented by (k+1)^2-k^2. All multiples 4k for k>1 can be represented by (k+1)^2-(k-1)^2. No number of the form 4k+2 is the difference of two squares because, modulo 4, the differences of two squares are 0, 1, or 3. [T. D. Noe, Apr 27 2009]

A024359(a(n)) = 0. - Reinhard Zumkeller, Nov 09 2012

Links

Table of n, a(n) for n=1..60.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Mathematica

a[1] = 1; a[2] = 2; a[3] = 4; a[n_] := 4*n-10; Array[a, 60] (* Jean-François Alcover, May 27 2015 *)

Prog

(Haskell)
a139544 n = a139544_list !! (n-1)
a139544_list = 1 : 2 : 4 : tail a016825_list
-- Reinhard Zumkeller, Nov 09 2012
(PARI) is(n)=n%4==2||n==1||n==4 \\ Charles R Greathouse IV, May 31 2013

Crossrefs

Cf. A024352, A016825.

Sequence in context: A345211 A125964 A288526 * A356959 A062091 A100143

Adjacent sequences: A139541 A139542 A139543 * A139545 A139546 A139547

Keyword

nonn,easy

Author

Artur Jasinski, Apr 25 2008

Extensions

Corrected by T. D. Noe, Apr 27 2009

Status

approved