A281384 Least integer with more than 1 digit in base n, such that the set of its base-n digits equals the set of its binary digits.

2, 9, 4, 5, 6, 49, 8, 9, 10, 11, 12, 13, 14, 225, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 961, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 3969, 64, 65, 66, 67, 68, 69, 70

Offset: 2

Author

Michel Marcus, Jan 21 2017

Keywords

• nonn

Comments

"More than 1 digit in base n" is equivalent to ">= n", which also implies "more than 1 digit in base 2", since n >= 2 by definition. If such a number written in binary is not a string of 1's, then its set of binary digits is {0, 1}, and the smallest number to have the same digits in base n is n = 10[n] itself. If n has all binary digits equal to 1, i.e., n = 2^k-1, then the smallest solution is the next larger number having the digits {0, 1} in base n (and also in base 2), which is, since 11[n] = n+1 is excluded, 100[n] = n^2 = (2^k-1)^2 = 2^{2k} + 2^{k+1} + 1 = 1...01[2]. - M. F. Hasler, Jan 22 2017

Crossrefs

First column of triangular array A281383.

Programs

PARI

a(n) = my(m=n); while (Set(digits(m, n)) != Set(digits(m,2)), m++); m;

PARI

A281384(n) = if(n+1==1<M. F. Hasler, Jan 22 2017

Formula

For any n>1: if n belongs to A000225, then a(n)=n^2, otherwise a(n)=n. - Rémy Sigrist, Jan 22 2017