A037089 Lexicographically earliest strictly increasing decimal autovarious sequence: a(n) = number of distinct n-digit endings (left-zero-padded) of terms in the sequence.

1, 2, 11, 12, 21, 22, 31, 32, 41, 42, 51, 101, 1001, 1002, 1011, 1012, 1021, 1022, 1031, 1032, 1041, 10001, 100001, 100002, 100011, 100012, 100021, 100022, 100031, 100032, 100041, 1000001, 10000001, 10000002, 10000011, 10000012

Offset

0,2

Comments

The first a(n) terms include all a(n) n-digit endings.

Links

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

Prog

(Python)
a, m, n, i = [1, 2, 11], 1, 1, 0
while len(a) <= 100:
    while (a[-1]==a[-2] or not all(len(set([x % (10 ** 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*(10**n))+a[i]
    if (len(a) in a): m, n, i = 1, n+1, 0; a.append((10**n)+1)
    else: a.append(a[-1])
a.pop(); print(a) # Dominic McCarty, Jan 29 2025

Crossrefs

Sequence in context: A096109 A136997 A085184 * A038118 A038117 A038116

Adjacent sequences: A037086 A037087 A037088 * A037090 A037091 A037092

Keyword

nonn,base,nice

Author

David W. Wilson

Status

approved