cp's OEIS Frontend

A230423 a(n) = smallest natural number x such that x=n+A034968(x), or zero if no such number exists.

%I A230423 #14 Nov 08 2013 13:47:23
%S A230423 0,2,4,0,0,6,8,10,0,0,12,14,16,0,0,18,20,22,0,0,0,0,0,24,26,28,0,0,30,
%T A230423 32,34,0,0,36,38,40,0,0,42,44,46,0,0,0,0,0,48,50,52,0,0,54,56,58,0,0,
%U A230423 60,62,64,0,0,66,68,70,0,0,0,0,0,72,74,76,0,0,78
%N A230423 a(n) = smallest natural number x such that x=n+A034968(x), or zero if no such number exists.
%C A230423 Also, if n can be partitioned into sum d1*(k1!-1) + d2*(k2!-1) + ... + dj*(kj!-1), where all k's are distinct and greater than one and each di is in range [1,ki] (in other words, if A230412(n)=1), then a(n) = d1*k1! + d2*k2! + ... + dj*kj!. If this is not possible, then n is one of the terms of A219658, and a(n)=0.
%H A230423 Antti Karttunen, <a href="/A230423/b230423.txt">Table of n, a(n) for n = 0..10079</a>
%F A230423 a(n) = 2*A230414(n).
%o A230423 (Scheme)
%o A230423 (define (A230423 n) (let loop ((k n)) (cond ((= (A219651 k) n) k) ((> k (+ n n)) 0) (else (loop (+ 1 k))))))
%Y A230423 a(A219650(n)) = A005843(n) = 2n. Cf. also A230414, A230424.
%Y A230423 Can be used to compute A230425-A230427.
%Y A230423 This sequence relates to the factorial base representation (A007623) in a similar way as A213723 relates to the binary system.
%K A230423 nonn
%O A230423 0,2
%A A230423 _Antti Karttunen_, Oct 31 2013