A331531 - OEIS

A331531

Numbers of the form (x^2) OR (y^2) with x, y >= 0 (where OR denotes the bitwise OR operator).

0, 1, 4, 5, 9, 13, 16, 17, 20, 25, 29, 36, 37, 45, 49, 52, 53, 57, 61, 64, 65, 68, 73, 80, 81, 85, 89, 100, 101, 109, 113, 116, 117, 121, 125, 144, 145, 148, 153, 169, 173, 177, 180, 185, 196, 197, 205, 208, 209, 212, 213, 221, 225, 228, 229, 233, 237, 241

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OFFSET

1,3

COMMENTS

All squares belong to the sequence.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

EXAMPLE

The first terms, alongside the corresponding decompositions, are:

n a(n) Corresponding (x, y) (with x<=y)

-- ---- -----------------------------------------

1 0 (0, 0)

2 1 (0, 1) (1, 1)

3 4 (0, 2) (2, 2)

4 5 (1, 2)

5 9 (0, 3) (1, 3) (3, 3)

6 13 (2, 3)

7 16 (0, 4) (4, 4)

8 17 (1, 4)

9 20 (2, 4)

10 25 (0, 5) (1, 5) (3, 4) (3, 5) (4, 5) (5, 5)

PROG

(PARI) is(n) = setsearch(setbinop(bitor, select(x2 -> bitand(n, x2)==x2, vector(1+sqrtint(n), x, (x-1)^2))), n)>0

CROSSREFS

Cf. A000290, A331534 (least x), A331535 (corresponding y).

Sequence in context: A006844 A022425 A277549 * A363319 A363267 A328223

Adjacent sequences: A331528 A331529 A331530 * A331532 A331533 A331534

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Jan 19 2020

STATUS

approved