A257262 - OEIS

%I #13 Feb 14 2024 01:05:32

%S 1,2,3,6,7,8,9,19,20,21,24,25,26,27,30,31,32,33,42,43,44,45,73,74,75,

%T 78,79,80,81,91,92,93,97,98,99,102,103,104,105,115,116,117,120,121,

%U 122,123,126,127,128,129,138,139,140,141,144,145,146,147,150,151,152,153,162,163,164,165,192,193,194,195,198,199,200,201

%N Numbers such that the least missing nonzero digit (A257079) in their factorial base representation is 2.

%H Antti Karttunen, <a href="/A257262/b257262.txt">Table of n, a(n) for n = 1..9361</a>

%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.

%e The factorial base representation (A007623) of 1 is "1", the least nonzero digit missing from that is 2, thus 1 is included in this sequence.

%e Likewise for 2, whose f.b.r. is "10", and also for  42 whose f.b.r. is "1300", the least nonzero digit missing from them is 2, thus also 2 and 42 are included in this sequence.

%t q[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; MemberQ[s, 1] && !MemberQ[s, 2]]; Select[Range[200], q] (* _Amiram Eldar_, Feb 14 2024 *)

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A257262 (MATCHING-POS 1 0 (lambda (n) (= 2 (A257079 n)))))

%Y Cf. A007623, A257079, A255411, A257263.

%Y Cf. A059590 (is a subsequence, apart from its zero-term).

%Y Subsequence of A256450.

%K nonn,base

%O 1,2

%A _Antti Karttunen_, Apr 27 2015