A380356 a(0) = 0, a(1) = 1, and for any n > 0, if a(n) is at square distance from the least integer (in absolute value) not yet in the sequence and of opposite sign to a(n), say u, then a(n+1) = u, otherwise a(n+1) = a(n) + sign(a(n)).

0, 1, 2, 3, -1, -2, -3, -4, -5, 4, 5, 6, 7, 8, 9, 10, -6, -7, -8, -9, -10, -11, -12, -13, -14, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35

Offset

0,3

Comments

This sequence is a variant of A377091 that, by design, contains every integer (positive or negative).

Positive values appear in increasing order, negative values appear in decreasing order.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program

Example

a(0) = 0 and a(1) = 1 by definition.
At this point, the least value (in absolute value) not yet in the sequence and of opposite sign is -1.
a(1) is not at square distance from -1, so a(2) = 1 + sign(1) = 2.
a(2) is not at square distance from -1, so a(3) = 2 + sign(2) = 3.
a(3) is at square distance from -1, so a(4) = -1.
At this point, the least value (in absolute value) not yet in the sequence and of opposite sign is 4.
a(4) is not at square distance from 4, so a(5) = -1 + sign(-1) = -2.

Prog

(PARI) \\ See Links section.

Crossrefs

See A380357 for a similar sequence.

Cf. A377091.

Sequence in context: A194107 A071797 A338027 * A025481 A124171 A276146

Adjacent sequences: A380352 A380354 A380355 * A380357 A380360 A380361

Keyword

sign,easy,new

Author

Rémy Sigrist, Jan 22 2025

Status

approved