

A227149


Numbers n for which the sum of digits is odd when n is written in the factorial base (A007623).


6



1, 2, 5, 6, 9, 10, 13, 14, 17, 18, 21, 22, 24, 27, 28, 31, 32, 35, 36, 39, 40, 43, 44, 47, 49, 50, 53, 54, 57, 58, 61, 62, 65, 66, 69, 70, 72, 75, 76, 79, 80, 83, 84, 87, 88, 91, 92, 95, 97, 98, 101, 102, 105, 106, 109, 110, 113, 114, 117, 118, 120, 123, 124
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OFFSET

1,2


COMMENTS

Numbers n for which minimal number of factorials needed to add to get n is odd.
This sequence offers one possible analog to A000069 (odious numbers) in factorial base system. A227132 gives another kind of analog.
In each range [0,n!1] exactly half of the integers are found in this sequence, and the other half of them are found in the complement, A227148.
The sequence gives the positions of odd permutations in the tables A055089 and A195663; and equivalently, the positions of odd numbers in A055091.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..2520
Wikipedia, Parity of permutation


PROG

(Scheme, with Antti Karttunen's IntSeqlibrary): (define A227149 (MATCHINGPOS 1 0 (lambda (i) (odd? (A034968 i)))))


CROSSREFS

Complement: A227148. Cf. also A000069, A034968, A055091, A227132.
Sequence in context: A085183 A133759 A188258 * A042963 A264120 A166097
Adjacent sequences: A227146 A227147 A227148 * A227150 A227151 A227152


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jul 02 2013


STATUS

approved



