A268384 Characteristic function of A001317.

0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0

Comments

a(k) = 1 iff k is in A001317, and 0 for all other values.

The recursive formula is based on the fact that only from the terms of A001317 we can reach all the way down to 1 when repeatedly applying the map k -> A006068(k)/2 as long as it is possible to iterate (before A006068(k) is odd).

This sequence is not multiplicative. The smallest counterexample is for n = A000215(6) = 4294967297 which is the first composite Fermat number. In this case a(n) = 1 which is not the product of a(641) and a(6700417) which are both zero. - Andrew Howroyd, Aug 08 2018

Links

Antti Karttunen, Table of n, a(n) for n = 0..4369

Index entries for characteristic functions

Formula

a(0) = 0, a(1) = 1, and for n > 1, a(n) = 0 if A006068(n) is odd, otherwise a(A006068(n)/2).

a(n) = A209229(A193231(n)).

Prog

(Scheme, two variants)
(definec (A268384 n) (cond ((<= n 1) n) ((odd? (A006068 n)) 0) (else (A268384 (/ (A006068 n) 2))))) ;; Uses the memoization-macro definec
(define (A268384 n) (A209229 (A193231 n)))
(Python)
from itertools import count, islice
def A268384_gen(): # generator of terms
    a = -1
    for n in count(0):
        b = int(''.join(str(int(not(~n&k))) for k in range(n+1)), 2)
        yield from (0, )*(b-a-1)
        yield 1
        a = b
A268384_list = list(islice(A268384_gen(), 30)) # Chai Wah Wu, Jun 30 2022

Crossrefs

Cf. A001317, A006068, A193231, A209229.

Cf. also A000215, A268389, A268391.

Sequence in context: A309752 A209355 A141743 * A358670 A288524 A112416

Adjacent sequences: A268381 A268382 A268383 * A268385 A268386 A268387

Keyword

nonn

Author

Antti Karttunen, Feb 10 2016

Status

approved