A262693 Characteristic function for A259934.

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, 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, 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

Offset

0

Comments

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

From Antti Karttunen, Nov 29 2015: (Start)

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.

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.

(End)

Links

Antti Karttunen, Table of n, a(n) for n = 0..65538

Formula

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

Prog

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

Crossrefs

Cf. A049820, A259934, A262694.

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

Sequence in context: A102242 A005369 A278169 * A267423 A108340 A341040

Adjacent sequences: A262690 A262691 A262692 * A262694 A262695 A262696

Keyword

nonn

Author

Antti Karttunen, Oct 04 2015

Status

approved