cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A097268 Numbers that are both the sum of two nonzero squares and the difference of two nonzero squares.

Original entry on oeis.org

5, 8, 13, 17, 20, 25, 29, 32, 37, 40, 41, 45, 52, 53, 61, 65, 68, 72, 73, 80, 85, 89, 97, 100, 101, 104, 109, 113, 116, 117, 125, 128, 136, 137, 145, 148, 149, 153, 157, 160, 164, 169, 173, 180, 181, 185, 193, 197, 200, 205, 208, 212, 221, 225, 229, 232, 233
Offset: 1

Views

Author

Ray Chandler, Aug 19 2004

Keywords

Comments

Intersection of A000404 (sum of squares) and A024352 (difference of squares).
Also: Numbers of the form x^2+4y^2, where x and y are positive integers. Cf. A154777, A092572, A154778 for analogous sequences. - M. F. Hasler, Jan 24 2009

Links

Crossrefs

Cf. A000404, A024352, A097269, A097270, A097271.

Programs

  • PARI
    isA097268(n) = forstep( b=2,sqrtint(n-1),2, issquare(n-b^2) && return(1)) \\ M. F. Hasler, Jan 24 2009

A097269 Numbers that are the sum of two nonzero squares but not the difference of two nonzero squares.

Original entry on oeis.org

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
Offset: 1

Views

Author

Ray Chandler, Aug 19 2004

Keywords

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

Examples

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

Links

Crossrefs

Cf. A000404, A024352, A097268, A097270, A097271. Equals twice A057653.
Cf. A020668, A263715.

Programs

  • 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

A097271 Numbers that are neither the sum of two nonzero squares nor the difference of two nonzero squares.

Original entry on oeis.org

1, 4, 6, 14, 22, 30, 38, 42, 46, 54, 62, 66, 70, 78, 86, 94, 102, 110, 114, 118, 126, 134, 138, 142, 150, 154, 158, 166, 174, 182, 186, 190, 198, 206, 210, 214, 222, 230, 238, 246, 254, 258, 262, 266, 270, 278, 282, 286, 294, 302, 310, 318, 322, 326, 330, 334
Offset: 1

Views

Author

Ray Chandler, Aug 19 2004

Keywords

Comments

Complement of union of A000404 (sum of squares) and A024352 (difference of squares).
Differs from A062316 only in having an initial 1,4.

Links

Crossrefs

Cf. A000404, A024352, A097268-A097270.

Programs

  • Mathematica
    Module[{nn=70,sq},sq=Flatten[{Total[#],Abs[#[[1]]-#[[2]]]}&/@Tuples[ Range[ 3nn]^2,2]]//Union;Take[Complement[Range[Max[sq]],sq],nn]] (* Harvey P. Dale, Nov 04 2016 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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