A213723 - OEIS

A213723

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

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 A213725-A213727. 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