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A212598 a(n) = n - m!, where m is the largest number such that m! <= n.

%I A212598 #16 Mar 18 2025 20:53:45
%S A212598 0,0,1,2,3,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,
%T A212598 7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
%U A212598 31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66
%N A212598 a(n) = n - m!, where m is the largest number such that m! <= n.
%C A212598 The m in definition is given by A084558(n).
%C A212598 Sequence consists of numbers 0..A001563(n)-1 followed by numbers 0..A001563(n+1)-1, and so on. - _Antti Karttunen_, Dec 17 2012
%H A212598 A. Karttunen, <a href="/A212598/b212598.txt">Table of n, a(n) for n = 1..5040</a>
%F A212598 a(n) = n-A000142(A084558(n)). - _Antti Karttunen_, Dec 17 2012
%p A212598 f:=proc(n) local i; for i from 0 to n do if i! > n then break; fi; od; n-(i-1)!; end;
%p A212598 [seq(f(n),n=1..70)];
%o A212598 (Scheme) (define (A212598 n) (- n (A000142 (A084558 n))))
%o A212598 (PARI) a(n)=my(m); while(m++!<=n,); n-(m-1)! \\ _Charles R Greathouse IV_, Sep 02 2015
%Y A212598 Cf. A136437, A212266, A220656.
%K A212598 nonn
%O A212598 1,4
%A A212598 _N. J. A. Sloane_, May 22 2012