A276090 Left inverse of A276089: For n = sum_{i=1..} d(i)*i! (with each d(i) <= i), a(n) = sum_{j=1..} d(2j-1)*j!.

0, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 6, 7, 0, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 6, 7, 0, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 6, 7, 0, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 6, 7, 0, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 6, 7, 6

Offset: 0

Author

Antti Karttunen, Aug 19 2016

Keywords

• nonn
• base

Comments

This "deaerates" A276089(n) by picking only the digits from the odd positions of its factorial base representation. Of course, when computed for an arbitrary n, those digits, when "compressed" into a(n) are not necessarily valid digits in standard factorial base representation (A007623).

Examples

			For n = 311 ("22321" in factorial base representation) we pick the digits at odd positions 1, 3 and 5, thus we get a(311) = 2*3! + 3*2! + 1*1! = 19.
For n=373 ("30201"), we pick the digits from those same positions and construct a(373) = 3*3! + 2*2! + 1*1! = 23.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..20533
• Index entries for sequences related to factorial base representation

Crossrefs

Left inverse of A276089.

For no apparent reason, the terms a(0)..a(21) are equal to the terms a(3)..a(24) of A118777.

Cf. A007623.

Formula

Other identities. For all n >= 0:

a(A276089(n)) = n.