

A213723


a(n) = smallest natural number x such that x=n+A000120(x), otherwise zero.


18



0, 2, 0, 4, 6, 0, 0, 8, 10, 0, 12, 14, 0, 0, 0, 16, 18, 0, 20, 22, 0, 0, 24, 26, 0, 28, 30, 0, 0, 0, 0, 32, 34, 0, 36, 38, 0, 0, 40, 42, 0, 44, 46, 0, 0, 0, 48, 50, 0, 52, 54, 0, 0, 56, 58, 0, 60, 62, 0, 0, 0, 0, 0, 64, 66, 0, 68, 70, 0, 0, 72, 74, 0, 76, 78
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OFFSET

0,2


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..1024


FORMULA

a(n) = 2*A213714(n).
Also, by partitioning into sums of distinct nonzero terms of A000225: if n can be formed as a sum of (2^a)1 + (2^b)1 + (2^c)1, etc. where the exponents a, b, c are distinct and all > 0, then a(n) = 2^a + 2^b + 2^c, etc. If this is not possible, then n is one of the terms of A055938, and a(n)=0.


EXAMPLE

a(1) = 2, as 2 is the smallest natural number such that x such that x=1+A000120(x) (as 2=1+A000120(2)=1+1).
a(2) = 0, as there are no solutions for 2, because it belongs to A055938.
a(11) = 14, as 14 is the smallest natural number x such that x=11+A000120(x) (as 14=11+A000120(14)=11+3).


PROG

(Scheme): (define (A213723 n) (A005843 (A213714 n)))
(Haskell)
a213723 = (* 2) . a213714  Reinhard Zumkeller, May 01 2015


CROSSREFS

a(A055938(n)) = 0. a(A005187(n)) = A005843(n) = 2n.
Cf. A213724. Used for computing A213725A213727. Cf. A179016.
Sequence in context: A121451 A265820 A096984 * A104601 A233673 A319931
Adjacent sequences: A213720 A213721 A213722 * A213724 A213725 A213726


KEYWORD

nonn


AUTHOR

Antti Karttunen, Nov 01 2012


STATUS

approved



