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%I #12 Apr 29 2015 13:35:03
%S 1,2,5,6,10,13,14,17,19,20,23,24,28,36,40,42,46,49,50,53,54,58,61,62,
%T 65,67,68,71,73,74,77,78,82,85,86,89,91,92,95,97,98,101,102,106,109,
%U 110,113,115,116,119,120,124,132,136,138,142,168,172,180,184,186,190,192,196,204,208,210
%N Numbers n such that there is exactly one 1 in their factorial base representation (A007623).
%H Antti Karttunen, <a href="/A255341/b255341.txt">Table of n, a(n) for n = 1..13069</a>
%e The factorial base representation (A007623) of 5 is "21", which contains exactly one 1, thus 5 is included in the sequence.
%e The f.b.r. of 23 is "321", with only one 1, thus 23 is included in the sequence.
%e The f.b.r. of 24 is "1000", with only one 1, thus 24 is included in the sequence.
%t factBaseIntDs[n_] := Module[{m, i, len, dList, currDigit}, i = 1; While[n > i!, i++]; m = n; len = i; dList = Table[0, {len}]; Do[currDigit = 0; While[m >= j!, m = m - j!; currDigit++]; dList[[len - j + 1]] = currDigit, {j, i, 1, -1}]; If[dList[[1]] == 0, dList = Drop[dList, 1]]; dList]; s = Table[FromDigits[factBaseIntDs[n]], {n, 210}]; {0}~Join~Flatten@ Position[s, x_ /; DigitCount[x][[1]] == 1] (* _Michael De Vlieger_, Apr 27 2015, after _Alonso del Arte_ at A007623 *)
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A255341 (MATCHING-POS 1 0 (lambda (n) (= 1 (A257511 n)))))
%Y Cf. A007623, A257511, A255411, A255342, A255343.
%Y Subsequence of A256450.
%Y Subsequences: A000142, A033312 (apart from its zero-terms).
%K nonn,base
%O 1,2
%A _Antti Karttunen_, Apr 27 2015
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