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Numbers that are >= k! but < 2*k! for some k; numbers whose factorial base representation (A007623) begins with digit "1".
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%I #17 Feb 18 2021 01:36:12

%S 1,2,3,6,7,8,9,10,11,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,

%T 40,41,42,43,44,45,46,47,120,121,122,123,124,125,126,127,128,129,130,

%U 131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150

%N Numbers that are >= k! but < 2*k! for some k; numbers whose factorial base representation (A007623) begins with digit "1".

%C Numbers k for which A099563(k) = 1.

%C Numbers k for which A265333(k) = 1.

%H Antti Karttunen, <a href="/A265334/b265334.txt">Table of n, a(n) for n = 1..5915</a>

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

%e 1 is present as 1 >= 1! but < 2*1!

%e 2 is present as 2 >= 2! but < 2*2!

%e 3 is present as 3 >= 2! but < 2*2!

%e 4 is not present as 4 >= 2! but not < 2*2! (and not >= 3!).

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

%o (define A265334 (NONZERO-POS 1 1 A265333))

%Y Cf. A007623, A099563, A265333 (characteristic function).

%Y Cf. A059590, A060112 (subsequences).

%Y Cf. also A265897, A265898.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 25 2015