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A262693 Characteristic function for A259934. 12


%S 1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,

%T 1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,

%U 0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1

%N Characteristic function for A259934.

%C Apart from a(0)=1 the first differences of A262694.

%C From _Antti Karttunen_, Nov 29 2015: (Start)

%C Provided that A259934 indeed is the unique infinite sequence s satisfying the condition A049820(s(k)) = s(k-1) for all k>=1, then the alternative but equivalent definition for this sequence is: a(n) = 0 if there are only finitely many integers from which one can reach n by repeated iterations of A049820, and 1 otherwise.

%C In case A259934 were not a unique solution, but only the lexicographically earliest branch of several, then the above alternative definition would produce more 1's after some (large) value of n. It would also be a more appropriate definition for the sequences like A262522 (A262896) and A262695 - A262697 (to keep them well-defined in principle), than the current, more restricted definition of this sequence.

%C (End)

%H Antti Karttunen, <a href="/A262693/b262693.txt">Table of n, a(n) for n = 0..65538</a>

%F a(0) = 1; for n >= 1, a(n) = A262694(n) - A262694(n-1).

%o (define (A262693 n) (if (zero? n) 1 (- (A262694 n) (A262694 (- n 1)))))

%Y Cf. A049820, A259934, A262694.

%Y Cf. also A262522, A262695, A262696, A262697, A262896, A262897.

%K nonn

%O 0

%A _Antti Karttunen_, Oct 04 2015

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Last modified November 21 12:28 EST 2019. Contains 329370 sequences. (Running on oeis4.)