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A023745 Plaindromes: numbers whose digits in base 3 are in nondecreasing order. 9
0, 1, 2, 4, 5, 8, 13, 14, 17, 26, 40, 41, 44, 53, 80, 121, 122, 125, 134, 161, 242, 364, 365, 368, 377, 404, 485, 728, 1093, 1094, 1097, 1106, 1133, 1214, 1457, 2186, 3280, 3281, 3284, 3293, 3320, 3401, 3644, 4373, 6560, 9841, 9842, 9845, 9854 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

A. V. Kitaev, Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin, arXiv:1809.00122 [math.CA], 2018.

FORMULA

Numbers that in ternary are the concatenation of i 1's with j 2's, i, j>=0. Also a(n) = A073216(n+1) - 1. Proof: Write a(n) as 1{m}2{n}, then adding 1 gives 1{m-1}20{n} for m>0 and 10{n} for m=0. Doubling yields 10{m-1}10{n} or 20{n}, respectively. These two forms exactly describe the forms of sums of two powers of 3, the two powers being 3^n and 3^(m+n). - Hugo van der Sanden

EXAMPLE

In base 3 these numbers are 0, 1, 2, 11, 12, 22, 111, 112, 122, 222, 1111, 1112, ... [corrected by Sean A. Irvine, Jun 10 2019]

MATHEMATICA

Select[Range[0, 10000], !Negative[Min[Differences[IntegerDigits[ #, 3]]]]&] (* or *) With[{nn=10}, FromDigits[#, 3]&/@Union[Flatten[Table[ PadRight[ PadLeft[{}, n, 1], x, 2], {n, 0, nn}, {x, 0, nn}], 1]]] (* Harvey P. Dale, Oct 12 2011 *)

Select[Range[0, 10000], LessEqual@@IntegerDigits[#, 3]&] (* Ray Chandler, Jan 06 2014 *)

CROSSREFS

Cf. A023746 onwards. In base 2 we get A000225.

Sequence in context: A334522 A102829 A031988 * A217136 A294944 A178656

Adjacent sequences:  A023742 A023743 A023744 * A023746 A023747 A023748

KEYWORD

nonn,base,easy

AUTHOR

Olivier Gérard

EXTENSIONS

Change offset to 1 by Ray Chandler, Jan 06 2014

STATUS

approved

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Last modified October 16 22:31 EDT 2021. Contains 348047 sequences. (Running on oeis4.)