A158022 Integers k such that all the digits needed to write the consecutive nonnegative integers from 0 to k fill exactly a square (no holes, no overlaps).

0, 3, 8, 12, 22, 36, 54, 76, 101, 121, 132, 156, 169, 197, 212, 244, 261, 297, 316, 356, 377, 421, 444, 492, 517, 569, 596, 652, 681, 741, 772, 836, 869, 937, 972, 10221, 10626, 11041, 11466, 11901, 12346, 12801, 13266, 13741, 14226, 14721, 15226

Offset

1,2

Comments

The sides of the successive squares are given by A158023. Terms computed by Jean-Marc Falcoz.

Integers k such that A058183(k)+1 is a square. - Dominic McCarty, Mar 28 2025

Links

Dominic McCarty, Table of n, a(n) for n = 1..10000

Eric Angelini, Digit Spiral

Eric Angelini, Digit Spiral [Cached copy, with permission]

Example

...0...01...012...0123...012345
.......23...345...4567...678910
............678...8910...111213
..................1112...141516
.........................171819
.........................202122
The integers fitting exactly in the SE corner of the above squares are 0, 3, 8, 12, 22. There is no 5x5 square where this is possible.

Prog

(Python)
from math import isqrt
a, k, l = [], 0, 0
while len(a) < 40:
    l += len(str(k))
    if l == isqrt(l) ** 2: a.append(k)
    k += 1
print(a) # Dominic McCarty, Mar 28 2025

Crossrefs

Cf. A058183, A158023.

Sequence in context: A022407 A330897 A169923 * A209934 A007434 A379717

Adjacent sequences: A158019 A158020 A158021 * A158023 A158024 A158025

Keyword

base,nonn

Author

Eric Angelini, Mar 11 2009

Status

approved