A382945 a(n) is the least positive integer k having a divisor d such that k/d is not a power of n and the base n expansions of k and d, possibly with leading zeros, have, up to order, the same digits.
9, 28, 18, 16, 40, 36, 42, 64, 105, 45, 154, 105, 130, 168, 260, 120, 340, 96, 266, 275, 495, 231, 460, 351, 450, 273, 792, 175, 928, 280, 682, 1024, 308, 459, 1302, 741, 962, 665, 1612, 288, 1804, 560, 1290, 1265, 2139, 1035, 1974, 540, 952, 715, 2720, 585
Offset: 2
Examples
The first terms, alongside an appropriate divisor d, in bases 10 and n, are: n a(n) d a(n) in base n d in base n -- ---- --- -------------- ----------- 2 9 3 1,0,0,1 1,1 3 28 4 1,0,0,1 1,1 4 18 6 1,0,2 1,2 5 16 8 3,1 1,3 6 40 10 1,0,4 1,4 7 36 12 5,1 1,5 8 42 21 5,2 2,5 9 64 16 7,1 1,7 10 105 15 1,0,5 1,5 11 45 15 4,1 1,4 12 154 22 1,0,10 1,10 13 105 21 8,1 1,8 14 130 65 9,4 4,9 15 168 56 11,3 3,11 16 260 20 1,0,4 1,4
Links
- Rémy Sigrist, Table of n, a(n) for n = 2..2501
Programs
-
PARI
a(n) = { for (k = 1, oo, my (t = vecsort(select(sign, digits(k, n)))); fordiv (k, d, if ((k/d) != n^valuation(k/d, n) && vecsort(select(sign, digits(d, n)))==t, return (k);););); }
Formula
a(n) <= n^3 + 1.
Comments