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A158030 Triangular numbers t such that all the digits needed to write the consecutive triangular numbers from 0 to t fill exactly an equilateral triangle (no holes, no overlaps). 1
0, 3, 10, 21, 153, 210, 378, 496, 820, 1431, 3081, 4656, 8646, 11628, 15051, 17766, 22578, 26335, 32896, 37950, 46665, 53301, 64620, 73153, 87571, 98346, 108345, 113526, 130305, 162735, 185136, 193131, 218791, 267546, 300700, 312445, 349866 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sides of the successive triangles are given by A158031. Terms computed by Jean-Marc 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. 84-85.

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. 324-325.

LINKS

Table of n, a(n) for n=1..37.

Eric Angelini, Digit Spiral

E. Angelini, Digit Spiral [Cached copy, with permission]

EXAMPLE

...0....0....0.....0

........13...13....13

.............610...610

...................1521

The triangular numbers fitting exactly in the SE corner of the above triangles are 0, 3, 10, 21.

CROSSREFS

Sequence in context: A120109 A286067 A337623 * A068082 A058077 A161672

Adjacent sequences:  A158027 A158028 A158029 * A158031 A158032 A158033

KEYWORD

base,nonn

AUTHOR

Eric Angelini, Mar 11 2009

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)