A285385 Positions of 1 in A285384; complement of A072939.

1, 2, 4, 5, 6, 8, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22, 24, 26, 28, 29, 30, 32, 34, 36, 37, 38, 40, 42, 44, 45, 46, 48, 49, 50, 52, 53, 54, 56, 58, 60, 61, 62, 64, 65, 66, 68, 69, 70, 72, 74, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 90, 92, 93, 94, 96, 98

Offset: 1

Author

Clark Kimberling, Apr 26 2017

Keywords

• nonn
• easy

Examples

			As a word, A285384 = 11011101..., in which the positions of 1 are 1,2,4,5,6,8,...
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A072939, A171946, A285384.

Programs

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 1}}] &, {0}, 16] (* A285384 *)
Flatten[Position[s, 0]]  (* A072939 *)
Flatten[Position[s, 1]]  (* A285385 *)

Python

def A285385(n):
    def f(x):
        c, s = n, bin(x-1)[2:]
        l = len(s)
        for i in range(l&1,l,2):
            c += int(s[i])+int('0'+s[:i],2)
        return c
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Jan 29 2025

Formula

a(n) = A171946(n) for n>=2.

a(n + 1) = a(n) + A096268(a(n) - 1) + 1 for all n > 0. (conjecture) - Velin Yanev, Mar 23 2019