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!)
A097269 Numbers that are the sum of two nonzero squares but not the difference of two nonzero squares. 14
2, 10, 18, 26, 34, 50, 58, 74, 82, 90, 98, 106, 122, 130, 146, 162, 170, 178, 194, 202, 218, 226, 234, 242, 250, 274, 290, 298, 306, 314, 338, 346, 362, 370, 386, 394, 410, 442, 450, 458, 466, 482, 490, 514, 522, 530, 538, 554, 562, 578, 586, 610, 626, 634 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A000404 (sum of squares) and complement of A024352 (difference of squares).

Numbers of the form 4k+2 = double of an odd number, with the odd number equal to the sum of 2 squares (sequence A057653). - Jean-Christophe Hervé, Oct 24 2015

Numbers that are the sum of two odd squares. - Jean-Christophe Hervé, Oct 25 2015

LINKS

Table of n, a(n) for n=1..54.

Eric Weisstein's World of Mathematics, Sum of Squares Function.

EXAMPLE

2 = 1^2 + 1^2, 10 = 1^2 + 3^2, 18 = 3^2 + 3^2.

PROG

(PARI) is(n)=if(n%4!=2, return(0)); my(f=factor(n/2)); for(i=1, #f[, 1], if(bitand(f[i, 2], 1)==1&&bitand(f[i, 1], 3)==3, return(0))); 1 \\ Charles R Greathouse IV, May 31 2013

(Python)

from itertools import count, islice

from sympy import factorint

def A097269_gen(): # generator of terms

    return filter(lambda n:all(p & 3 != 3 or e & 1 == 0 for p, e in factorint(n//2).items()), count(2, 4))

A097269_list = list(islice(A097269_gen(), 30)) # Chai Wah Wu, Jun 28 2022

CROSSREFS

Cf. A000404, A024352, A097268, A097270, A097271. Equals twice A057653.

Cf. A020668, A263715.

Sequence in context: A069081 A126005 A017089 * A304054 A028413 A282226

Adjacent sequences:  A097266 A097267 A097268 * A097270 A097271 A097272

KEYWORD

nonn,changed

AUTHOR

Ray Chandler, Aug 19 2004

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 7 00:24 EDT 2022. Contains 355115 sequences. (Running on oeis4.)