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A230422 Positions of ones in A230410.

%I A230422 #21 Jun 29 2016 00:08:35
%S A230422 1,8,14,16,18,22,33,35,37,41,45,51,53,57,61,71,75,82,87,96,106,116,
%T A230422 118,120,124,128,134,136,140,144,154,158,165,170,179,189,198,200,206,
%U A230422 208,212,216,226,230,237,242,251,261,270,272,280,289,293,300,305,314,324
%N A230422 Positions of ones in A230410.
%C A230422 This sequence gives all n at which positions the successive terms A219666(n-1) & A219666(n) in the infinite trunk of the factorial beanstalk differ only in one digit position in their factorial base representations (A007623).
%C A230422 Please see further comments and examples in A230410.
%H A230422 Antti Karttunen, <a href="/A230422/b230422.txt">Table of n, a(n) for n = 1..17517</a>
%F A230422 For all n, A230406(a(n)) is one of the terms of A051683.
%e A230422 14 is included, because A219666(13) = 40 = '1220' in factorial base representation, while A219666(14) = 46 = '1320' in factorial base, and they differ only by their third least significant digit.
%e A230422 16 is included, because A219666(15) = 48 = '2000' in factorial base representation, while A219666(16) = 52 = '2020' in factorial base, and they differ only by their second least significant digit.
%t A230422 nn = 10^4; m = 1; While[m! < Floor[6 nn/5], m++]; m; f[n_] := IntegerDigits[n, MixedRadix[Reverse@ Range[2, m]]]; Position[#, 1] &[Function[w, Count[Subtract @@ Map[PadLeft[#, Max@ Map[Length, w]] &, w], k_ /; k != 0]]@ Map[f@ # &, {#1, #2}] & @@@ Partition[#, 2, 1] &@ TakeWhile[Reverse@ NestWhileList[# - Total@ f@ # &, Floor[6 nn/5], # > 0 &], # <= nn &]] // Flatten (* _Michael De Vlieger_, Jun 27 2016, Version 10.2 *)
%o A230422 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A230422 (define A230422 (MATCHING-POS 1 1 (lambda (i) (= 1 (A230410 i)))))
%Y A230422 Subset: A231718. Cf. also A230410 and A258010 (first differences).
%K A230422 nonn
%O A230422 1,2
%A A230422 _Antti Karttunen_, Nov 10 2013