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a(n) = smallest natural number x such that x=n+A034968(x), or zero if no such number exists.
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%I #14 Nov 08 2013 13:47:23

%S 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 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 60,62,64,0,0,66,68,70,0,0,0,0,0,72,74,76,0,0,78

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

%C 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 Antti Karttunen, <a href="/A230423/b230423.txt">Table of n, a(n) for n = 0..10079</a>

%F a(n) = 2*A230414(n).

%o (Scheme)

%o (define (A230423 n) (let loop ((k n)) (cond ((= (A219651 k) n) k) ((> k (+ n n)) 0) (else (loop (+ 1 k))))))

%Y a(A219650(n)) = A005843(n) = 2n. Cf. also A230414, A230424.

%Y Can be used to compute A230425-A230427.

%Y This sequence relates to the factorial base representation (A007623) in a similar way as A213723 relates to the binary system.

%K nonn

%O 0,2

%A _Antti Karttunen_, Oct 31 2013