A307102 Numbers written in base of double factorial numbers (A006882).

1, 10, 100, 101, 110, 200, 201, 1000, 1001, 1010, 1100, 1101, 1110, 1200, 10000, 10001, 10010, 10100, 10101, 10110, 10200, 10201, 11000, 11001, 11010, 11100, 11101, 11110, 11200, 20000, 20001, 20010, 20100, 20101, 20110, 20200, 20201, 21000

Offset: 1

Author

Sean A. Irvine, Mar 24 2019

Keywords

• nonn
• base

Comments

a(1122755752855713895623244049306709034778906250) is the first term which cannot be included in the OEIS since it includes a non-decimal digit. - Charles R Greathouse IV, Sep 19 2012

Numbers in this mixed-radix number system can have multiple representations, so to avoid ambiguity this sequence assumes a greedy approach where leading digits are made as high as possible; thus we choose a(30) = 20000 rather than a(30) = 11201. - Sean A. Irvine, Mar 24 2019

Examples

			The digits (from right to left) have values 1, 2, 3, 8, 15, etc. (A006882), hence a(29) = 11200 because 29 = 1*15 + 1*8 + 2*3 + 0*2 + 0*1.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..10000
• F. Iacobescu, Smarandache Partition Type and Other Sequences, Bull. Pure Appl. Sciences, Vol. 16E, No. 2 (1997), pp. 237-240.
• Sean A. Irvine, Java program (github).
• F. Smarandache, Collected Papers, Vol. II.
• F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.
• Eric Weisstein's World of Mathematics, Smarandache Sequences.
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A006882 (double factorial numbers), A007623 (factorial base), A019513 (erroneous version).

Programs

Mathematica

a[n_] := FromDigits[NumberDecompose[n, Range[n, 1, -1]!!]]; Array[a, 40] (* Amiram Eldar, May 11 2024 *)