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%I #25 Nov 11 2016 19:57:44
%S 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,
%T 66,67,72,74,76,78,84,86,88,90,92,94,96,97,98,100,101,102,103,108,110,
%U 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
%N Numbers with hit-free factorial base representations; positions of zeros in A276004 & A276007.
%C 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 "hit-free" 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.
%C 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 non-singleton cycles of the permutation listed as n-th permutation in the list A060117 (or A060118).
%C This can be viewed as a factorial base analog of base-2 related A003714.
%H Antti Karttunen, <a href="/A276005/b276005.txt">Table of n, a(n) for n = 0..4140</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F Other identities. For all n >= 1:
%F a(A000110(n)) = n! = A000142(n). [To be proved.]
%e n=14 (factorial base "210") is included because 2 occurs in position 3 and 1 occurs in position 2, thus as (3-2) = 1 <> 2, 2 does not "hit" digit 1.
%e n=15 ("211") is NOT included because 2 occurring in position 3 hits the rightmost 1 in position 1 (as 3-2 = 1), and moreover, also the middle 1 hits the rightmost 1 as 2-1 = 1.
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A276005 (ZERO-POS 0 0 A276004))
%Y Complement: A276006.
%Y Cf. A000110, A000142, A060128, A060502, A276004, A276007.
%Y Cf. A060112 (a subsequence).
%Y Intersection with A275804 gives A261220.
%Y Cf. also A003714, A060117 and A060118.
%K nonn,base
%O 0,3
%A _Antti Karttunen_, Aug 17 2016
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