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

Author

Eric Angelini, Mar 11 2009

Keywords

• base
• nonn

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

Examples

			...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.
		

Links

• Dominic McCarty, Table of n, a(n) for n = 1..10000
• Eric Angelini, Digit Spiral
• Eric Angelini, Digit Spiral [Cached copy, with permission]

Crossrefs

Cf. A058183, A158023.

Programs

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