

A276005


Numbers with hitfree factorial base representations; positions of zeros in A276004 & A276007.


8



0, 1, 2, 4, 5, 6, 7, 12, 14, 16, 18, 19, 20, 22, 23, 24, 25, 26, 28, 29, 48, 49, 54, 55, 60, 66, 67, 72, 74, 76, 78, 84, 86, 88, 90, 92, 94, 96, 97, 98, 100, 101, 102, 103, 108, 110, 112, 114, 115, 116, 118, 119, 120, 121, 122, 124, 125, 126, 127, 132, 134, 136, 138, 139, 140, 142, 143, 240, 241, 242, 244, 245, 264, 265, 266, 268, 269, 288, 289, 312, 314, 316
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OFFSET

0,3


COMMENTS

We say there is a "hit" in factorial base representation (A007623) of n when there is any such pair of nonzero digits d_i and d_j in positions i > j so that (i  d_i) = j. Here the rightmost (least significant digit) occurs at position 1. This sequence gives all "hitfree" numbers, meaning that for every nonzero digit d_i (in position i) in their factorial base representation the digit at the position (i  d_i) is 0.
Also numbers n for which A060502(n) = A060128(n), in other words, the numbers n for which the number of slopes in their factorial base representation (A007623) is equal to the number of nonsingleton cycles of the permutation listed as nth permutation in the list A060117 (or A060118).
This can be viewed as a factorial base analog of base2 related A003714.


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..4140
Index entries for sequences related to factorial base representation


FORMULA

Other identities. For all n >= 1:
a(A000110(n)) = n! = A000142(n). [To be proved.]


EXAMPLE

n=14 (factorial base "210") is included because 2 occurs in position 3 and 1 occurs in position 2, thus as (32) = 1 <> 2, 2 does not "hit" digit 1.
n=15 ("211") is NOT included because 2 occurring in position 3 hits the rightmost 1 in position 1 (as 32 = 1), and moreover, also the middle 1 hits the rightmost 1 as 21 = 1.


PROG

(Scheme, with Antti Karttunen's IntSeqlibrary)
(define A276005 (ZEROPOS 0 0 A276004))


CROSSREFS

Complement: A276006.
Cf. A000110, A000142, A060128, A060502, A276004, A276007.
Cf. A060112 (a subsequence).
Intersection with A275804 gives A261220.
Cf. also A003714, A060117 and A060118.
Sequence in context: A300861 A039057 A317185 * A092058 A134532 A282278
Adjacent sequences: A276002 A276003 A276004 * A276006 A276007 A276008


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Aug 17 2016


STATUS

approved



