A393218 Integers m such that the digits 0 and 1 are not present in the decimal expansion of m^10.

5, 7, 14, 118, 976, 71637, 703138, 1748922, 2306124, 3035514, 4510376, 4890662, 11549846, 19627862, 35969473, 62327367, 294747746, 453444795, 2177578246, 2318225513, 2336754337, 3475759083, 9446174268, 9871582464, 10908987136, 18358804965, 38170692864, 89504331973, 118755081435, 119536047158

Offset

1,1

Comments

a(n)^10 and 10^a(n) are in A393217, for all n >= 1.

Are there infinitely many terms in this sequence?

Links

Chai Wah Wu, Table of n, a(n) for n = 1..38

Example

5 is a term since 5^10 = 9765625 and the digits 0 and 1 are not present in its decimal expansion.

Mathematica

q[m_]:=ContainsNone[IntegerDigits[m^10], {0, 1}]; Select[Range[10^6], q] (* James C. McMahon, Feb 12 2026 *)

Prog

(PARI) isok(m) = vecmin(digits(m^10)) > 1; \\ Michel Marcus, Feb 07 2026
(Python)
from gmpy2 import digits, mpz
def ok(k): return k%10>1 and "0" not in (s:=digits(mpz(k)**mpz(10))) and "1" not in s
print([k for k in range(10**7) if ok(k)]) # Michael S. Branicky, Feb 07 2026

Crossrefs

Cf. A393217, A008454.

Sequence in context: A030755 A393127 A374811 * A373113 A170827 A314354

Adjacent sequences: A393215 A393216 A393217 * A393219 A393220 A393221

Keyword

nonn,base

Author

Gonzalo Martínez, Feb 06 2026

Extensions

a(19)-a(30) from Michael S. Branicky, Feb 07 2026

Status

approved