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

Author

Artur Jasinski, Apr 25 2008

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A024352, A016825.

Programs

Haskell

a139544 n = a139544_list !! (n-1)
a139544_list = 1 : 2 : 4 : tail a016825_list
-- Reinhard Zumkeller, Nov 09 2012

Mathematica

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

PARI

is(n)=n%4==2||n==1||n==4 \\ Charles R Greathouse IV, May 31 2013

Python

def A139544(n): return 1<Chai Wah Wu, Feb 11 2025

Extensions

Corrected by T. D. Noe, Apr 27 2009