A139544 - OEIS

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

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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