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

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

Offset: 0

Author

Antti Karttunen, Oct 31 2013

Keywords

• nonn

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10079

Crossrefs

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

Can be used to compute A230425-A230427.

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

Programs

Scheme

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

Formula

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