A178246 Numbers m such that all digits of m, including repetitions, occur among the digits of 2^m.

6, 10, 14, 17, 21, 25, 27, 28, 29, 30, 31, 35, 36, 37, 39, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 56, 57, 58, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117

Offset: 1

Author

Michel Lagneau, Dec 20 2010

Keywords

• nonn
• base

Comments

The sequence shows subsets of consecutive numbers.

153 is assumed to be the largest integer missing in this sequence. - Alois P. Heinz, Jan 28 2022

Examples

			17 is a term because the digits 1 and 7 are included in the number 2^17 = 131072;
3 is not a term because the digit 3 is not in the number 2^3 = 8.
33 is not a term because 2^33 = 8589934592 does not have 2 digits 3.
153 is not in the sequence because the digit 3 is not in the number 2^153 = 11417981541647679048466287755595961091061972992.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..962

Crossrefs

Cf. A000079, A064827, A032740.

Programs

Mathematica

Reap[Do[a = DigitCount[2^n]; b = DigitCount[n]; If[Min[a-b] >= 0, Sow[n]], {n, 10^3}]][[2, 1]]

PARI

isok(m) = {my(d=digits(m), dd=digits(2^m)); for (i=0, 9, if (#select(x->(x==i), d) > #select(x->(x==i), dd), return (0));); return(1);} \\ Michel Marcus, Jan 28 2022

Extensions

Name clarified by Michel Marcus, Jan 30 2022