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A158031 Sides of equilateral triangles which are filled exactly (no holes, no overlaps) by the digits used to write a subsequence of consecutive triangular numbers, starting with 0. 1

%I #9 Jul 07 2023 14:40:50

%S 1,2,3,4,8,9,11,12,14,17,22,25,30,33,36,38,41,43,46,48,51,53,56,58,61,

%T 63,65,66,69,74,77,78,81,86,89,90,93,98,101,102,105,110,113,114,117,

%U 122,125,126,132,133,139,140,146,147,153,154,160,161,167,168,174,175,181

%N Sides of equilateral triangles which are filled exactly (no holes, no overlaps) by the digits used to write a subsequence of consecutive triangular numbers, starting with 0.

%C The triangular numbers fitting exactly in a "triangulars-digits triangle" are given by A158030. 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....0....0.....0

%e ........13...13....13

%e .............610...610

%e ...................1521

%e The above "equilateral" triangles, filled exactly by a subsequence of consecutive triangular numbers starting with 0 have sides 1, 2, 3, 4. The next properly filled triangle will have side 8.

%K base,nonn

%O 1,2

%A _Eric Angelini_, Mar 11 2009

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