A361978 Complement of A361337.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 53, 57, 61, 62, 63, 64, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77, 79, 81, 82, 83, 84, 86, 88, 89, 91, 92, 93, 94, 97, 98, 99, 111, 112, 113, 114, 116

Offset: 1

Author

Michael S. Branicky, Apr 02 2023

Keywords

• nonn
• base

Comments

More than the usual number of terms are shown to distinguish the sequence from A034048.

Appears to be finite with 219 members, the largest being 3111.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..219

Crossrefs

Cf. A034048, A011540, A361337, A277061.

Subsequence of A052382.

Programs

PARI

A361978=select( {is_A361978(n)=vecmin(digits(n))&& !for(p=1, logint(n, 10), is_A361978(vecprod(divrem(n, 10^p)))|| return)}, [1..10^5]) \\ Conjecturedly the full list: no terms between 3112 and 10^5. - M. F. Hasler, Apr 05 2023

Python

def ok(n):
    if n < 10: return n != 0
    s = str(n)
    if "0" in s: return False
    return all(ok(int(s[:i])*int(s[i:])) for i in range(1, len(s)))
print([k for k in range(117) if ok(k)]) # Michael S. Branicky, Apr 02 2023