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a(n) = smallest natural number x such that x=n+A000120(x), otherwise zero.
18

%I #16 Aug 11 2015 01:13:40

%S 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,

%T 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,

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

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

%H Antti Karttunen, <a href="/A213723/b213723.txt">Table of n, a(n) for n = 0..1024</a>

%F a(n) = 2*A213714(n).

%F 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.

%e 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).

%e a(2) = 0, as there are no solutions for 2, because it belongs to A055938.

%e a(11) = 14, as 14 is the smallest natural number x such that x=11+A000120(x) (as 14=11+A000120(14)=11+3).

%o (Scheme): (define (A213723 n) (A005843 (A213714 n)))

%o (Haskell)

%o a213723 = (* 2) . a213714 -- _Reinhard Zumkeller_, May 01 2015

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

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

%K nonn

%O 0,2

%A _Antti Karttunen_, Nov 01 2012