A037091 Lexicographically earliest strictly increasing base 3 autovarious sequence: a(n) = number of distinct a(k) mod 3^n (written in base 3).

1, 2, 11, 12, 101, 1001, 1002, 1011, 1012, 1101, 10001, 10002, 10011, 10012, 10101, 11001, 11002, 11011, 11012, 11101, 20001, 20002, 20011, 20012, 20101, 21001, 21002, 21011, 100001, 1000001, 1000002, 10000001, 100000001, 100000002

Offset

0,2

Comments

The first a(n) elements include all a(n) residues mod 3^n.

Links

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

Prog

(Python)
a, m, n, i, b = [1, 2, 4], 1, 1, 0, 3
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();
def tern(n):
    if n == 0: return ""
    return tern(n // 3) + str(n % 3)
for k in a: print(tern(k)) # Dominic McCarty, Jan 29 2025

Crossrefs

Cf. A037090.

Sequence in context: A034118 A140148 A117547 * A289675 A127303 A378841

Adjacent sequences: A037088 A037089 A037090 * A037092 A037093 A037094

Keyword

nonn,base

Author

David W. Wilson

Status

approved