A275533 Least positive number m such that m^k for k = 1..n have no digit 1.

2, 2, 2, 74, 94, 305, 2975

Offset: 1

Author

Zak Seidov, Jul 31 2016

Keywords

• nonn
• base
• more
• fini

Comments

It appears that there are no more terms in this sequence.

If they exist, a(8) > 127231981 and a(9) > 107895940. - J.W.L. (Jan) Eerland, Nov 26 2022

If they exist, a(8)-a(15) > 10^13 and a(16) > 10^32; a(17) and beyond do not exist. - Michael S. Branicky, Apr 05 2024

Examples

			2975^k, k = 1..7 = 2975, 8850625, 26330609375, 78333562890625, 233042349599609375, 693300990058837890625, 2062570445425042724609375 (all are oneless), while 2975^8 = 6136147075139502105712890625 has 5 ones.
		

Crossrefs

Cf. A052383 (numbers without 1 as a digit), A371706.

Programs

Mathematica

Table[{n,m=1;Monitor[Parallelize[While[True,If[Length[DeleteCases[Table[If[MemberQ[IntegerDigits[m^k],1]==False,k,a],{k,1,n}],a]]==n,Break[]];m++];m],m]},{n,1,7}] (* J.W.L. (Jan) Eerland, Nov 26 2022 *)

Python

from itertools import count
def A275533(n): return next(m for m in count(1) if not any('1' in str(m**k) for k in range(1,n+1))) # Chai Wah Wu, Apr 04 2024

Formula

a(n) <= a(n+1). - Michael S. Branicky, Apr 05 2024