A164766 Smallest number m such that exactly n odd numbers can be seen as proper subsequences of m in decimal representation.

1, 10, 13, 103, 113, 131, 135, 1013, 1031, 1035, 1135, 1231, 1235, 1351, 1357, 10325, 10213, 10135, 10235, 10315, 10351, 10357, 11357, 12431, 12135, 13251, 12315, 12351, 12357, 13571, 13579, 101315, 101235, 103057, 101351, 102431, 102353, 101357, 102135, 103257

Offset: 0

Author

Reinhard Zumkeller, Aug 25 2009

Keywords

• nonn
• base

Comments

For any term first occurrences of positive even digits (2, 4, 6, 8) are in order. First 2 (if any) before first 4. Any number with an even digit d has all positive even digits < d. Same goes for odd digits (1, 3, 5, 7, 9). - David A. Corneth, Apr 12 2025

Examples

			a(6) = 135 as 135 is the smallest number such that exactly 6 numbers can be seen as proper subsequences of digits of 135 (namely 1, 3, 5, 13, 15, 35). Note that 135 is no proper substring of 135. - _David A. Corneth_, Apr 12 2025
153 is no term as the first 5 is before the first 3 and 5 is a larger odd digit than 3. - _David A. Corneth_, Apr 12 2025
		

Links

• David A. Corneth, Table of n, a(n) for n = 0..991 (first 101 terms from Amiram Eldar, terms <= 10^10)
• David A. Corneth, PARI program

Crossrefs

Cf. A045888.

Programs

Mathematica

f[n_] := Count[Union[Most[Rest[Subsets[IntegerDigits[n]]]]], ?(First[#] > 0 && OddQ[Last[#]] &)]; seq[len] := Module[{s = Table[0, {len}], c = 0, m = 1, i}, While[c < len, i = f[m] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = m]; m++]; s]; seq[20] (* Amiram Eldar, Apr 12 2025 *)

PARI

\\ See Corneth link

Formula

A045888(a(n)) = n and A045888(m) <> n for m < a(n).

Extensions

Revised and a(25)-a(39) added by Amiram Eldar, Apr 12 2025