

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



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, 63, 65, 66, 69, 74, 77, 78, 81, 86, 89, 90, 93, 98, 101, 102, 105, 110, 113, 114, 117, 122, 125, 126, 132, 133, 139, 140, 146, 147, 153, 154, 160, 161, 167, 168, 174, 175, 181
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OFFSET

1,2


COMMENTS

The triangular numbers fitting exactly in a "triangularsdigits triangle" are given by A158030. Terms computed by JeanMarc Falcoz.


REFERENCES

Mohammad K. Azarian, A Trigonometric Characterization of Equilateral Triangle, Problem 336, Mathematics and Computer Education, Vol. 31, No. 1, Winter 1997, p. 96. Solution published in Vol. 32, No. 1, Winter 1998, pp. 8485.
Mohammad K. Azarian, Equating Distances and Altitude in an Equilateral Triangle, Problem 316, Mathematics and Computer Education, Vol. 28, No. 3, Fall 1994, p. 337. Solution published in Vol. 29, No. 3, Fall 1995, pp. 324325.


LINKS

Table of n, a(n) for n=1..63.
Eric Angelini, Digit Spiral
E. Angelini, Digit Spiral [Cached copy, with permission]


EXAMPLE

...0....0....0.....0
........13...13....13
.............610...610
...................1521
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.


CROSSREFS

Sequence in context: A111020 A002971 A157318 * A139461 A126421 A116111
Adjacent sequences: A158028 A158029 A158030 * A158032 A158033 A158034


KEYWORD

base,nonn


AUTHOR

Eric Angelini, Mar 11 2009


STATUS

approved



