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

Offset: 0

Author

Antti Karttunen, Nov 01 2012

Keywords

• nonn

Examples

			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).
		

Links

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

Crossrefs

a(A055938(n)) = 0. a(A005187(n)) = A005843(n) = 2n.

Cf. A213724. Used for computing A213725-A213727. Cf. A179016.

Programs

Haskell

a213723 = (* 2) . a213714  -- Reinhard Zumkeller, May 01 2015

Scheme

(define (A213723 n) (A005843 (A213714 n)))

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.