A270037 a(n) = Smallest m >= 3 containing no zeros when represented in any base from 3 through n.

4, 5, 7, 7, 13, 13, 13, 13, 13, 13, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157

Offset: 3

Author

Nathan Fox, Mar 09 2016

Keywords

• nonn
• base

Comments

It remains to be determined if the sequence is finite.

Every known term in this sequence is in A069575, and every term in A069575 is in this sequence.

Links

• Nathan Fox, Table of n, a(n) for n = 3..618

Crossrefs

Cf. A069575, A270027, A270038, A216192, A270039, A270040, A270041, A270042, A270043, A270044, A270045.

Programs

Mathematica

Table[SelectFirst[Range[3, 10^3], Total@ Map[Function[k, DigitCount[#, k, 0]], Range[3, n]] == 0 &], {n, 3, 80}] /. n_ /; MissingQ@ n -> Nothing (* Michael De Vlieger, Mar 10 2016, Version 10.2 *)

PARI

isok(m, n) = {for (b=3, n, if (! vecmin(digits(m, b)), return (0));); 1;}
a(n) = {my(m = 3); while (! isok(m,n), m++); m;} \\ Michel Marcus, Mar 10 2016