

A067270


Numbers m such that mth triangular number (A000217) ends in m.


1



0, 1, 5, 25, 625, 9376, 90625, 890625, 7109376, 12890625, 212890625, 1787109376, 81787109376, 59918212890625, 259918212890625, 3740081787109376, 56259918212890625, 256259918212890625, 7743740081787109376
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OFFSET

1,3


COMMENTS

Thanks to David W. Wilson for the proof that this sequence is a proper subset of A003226.
Also, numbers m such that the mth kgonal number ends in m for k == 1, 3, 5, or 9 (mod 10).  Robert Dawson, Jul 09 2018
This sequence is the intersection of A093534 and A301912.  Robert Dawson, Aug 01 2018


LINKS

Table of n, a(n) for n=1..19.
Robert Dawson, On Some Sequences Related to Sums of Powers, J. Int. Seq., Vol. 21 (2018), Article 18.7.6.


EXAMPLE

The 5th triangular = 15 ends in 5, hence 5 is a term of the sequence.


MATHEMATICA

(* a5=A018247 less the commas; a6=A018248 less the commas; *)
b5 = FromDigits[ Reverse[ IntegerDigits[a5]]]; b6 = FromDigits[ Reverse[ IntegerDigits[a6]]]; f[0] = 1; f[n_] := Block[{c5 = Mod[b5, 10^n], c6 = Mod[b6, 10^n]}, If[ Mod[c5(c5 + 1)/2, 10^n] == c5, c5, c6]]; Union[ Table[ f[n], {n, 0, 20}]]


CROSSREFS

Proper subset of A003226. Cf. A007185, A018247, A016090, A018248.
Intersection of A093534 and A301912.
Sequence in context: A007185 A175852 A030995 * A215118 A218150 A176594
Adjacent sequences: A067267 A067268 A067269 * A067271 A067272 A067273


KEYWORD

base,nonn


AUTHOR

Joseph L. Pe, Feb 21 2002


EXTENSIONS

Edited and extended by Robert G. Wilson v, Nov 20 2002
0 prepended by David A. Corneth, Aug 02 2018


STATUS

approved



