login
Integers n such that all the digits needed to write the consecutive nonnegative integers from 0 to n fill exactly a square (no holes, no overlaps).
10

%I #4 Jun 09 2016 21:42:42

%S 0,3,8,12,22,36,54,76,101,121,132,156,169,197,212,244,261,297,316,356,

%T 377,421,444,492,517,569,596,652,681,741,772,836,869,937,972,10221,

%U 10626,11041,11466,11901,12346,12801,13266,13741,14226,14721,15226

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

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

%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/DigitSpiral.htm">Digit Spiral</a>

%H E. Angelini, <a href="/A158022/a158022.pdf">Digit Spiral</a> [Cached copy, with permission]

%e ...0...01...012...0123...012345

%e .......23...345...4567...678910

%e ............678...8910...111213

%e ..................1112...141516

%e .........................171819

%e .........................202122

%e 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.

%K base,nonn

%O 1,2

%A _Eric Angelini_, Mar 11 2009