A037090 Lexicographically earliest strictly increasing base-2 autovarious sequence: a(n) = number of distinct a(k) mod 2^n (written in base 2).

1, 10, 11, 101, 110, 1001, 10001, 10010, 10011, 100001, 100010, 100011, 100101, 100110, 101001, 110001, 110010, 1000001, 10000001, 100000001, 100000010, 100000011, 100000101, 100000110, 100001001, 100010001, 100010010, 100010011

Offset

0,2

Comments

The first a(n) elements include all a(n) residues mod 2^n.

Links

Dominic McCarty, Table of n, a(n) for n = 0..1000

Prog

(Python)
a, m, n, i, b = [1, 2, 3, 5], 1, 2, 0, 2
while len(a) <= 100:
    while (a[-1]==a[-2] or not all(len(set([x % (b ** j) for x in a])) <= a[j] for j in range(1, len(a)-1))):
        i += 1
        if (i == len(a)-1):i, m = 0, m+1
        a[-1] = (m*(b**n))+a[i]
    if (len(a) in a): m, n, i = 1, n+1, 0; a.append((b**n)+1)
    else: a.append(a[-1])
a.pop();
for k in a: print(bin(k)[2:]) # Dominic McCarty, Jan 29 2025

Crossrefs

Cf. A037091.

Sequence in context: A205598 A350312 A368804 * A171676 A118240 A157845

Adjacent sequences: A037087 A037088 A037089 * A037091 A037092 A037093

Keyword

nonn,base

Author

David W. Wilson

Status

approved