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

0,2

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

Formula

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

Prog

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

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.

Sequence in context: A300324 A298368 A072069 * A213672 A309244 A004025

Adjacent sequences: A230420 A230421 A230422 * A230424 A230425 A230426

Keyword

nonn

Author

Antti Karttunen, Oct 31 2013

Status

approved