login
A372384
The smallest composite number k such that the digits of k and its prime factors, both written in base n, contain the same set of distinct digits.
5
4, 8, 30, 25, 57, 16, 27, 192, 132, 121, 185, 169, 465, 32, 306, 289, 489, 361, 451, 2250, 552, 529, 125, 1586, 81, 1652, 985, 841, 1057, 64, 1285, 86166, 2555, 1332, 1387, 1369, 4752, 3240, 2005, 1681, 2649, 1849, 2047, 5456, 2256, 2209, 343, 5050, 2761, 5876, 2862, 2809, 3097, 15512
OFFSET
2,1
LINKS
FORMULA
a(n) = 2*n + 2 if n = 2^k - 1 with k >= 2, otherwise a(n) = n^2 if n is prime.
EXAMPLE
a(4) = 30 as 30 = 2 * 3 * 5 = 132_4 = 2_4 * 3_4 * 11_4, and both 132_4 and its primes factors contain the same distinct digits 1, 2, and 3.
a(10) = 132 as 132 = 2 * 3 * 11, and both 132 and its primes factors contain the same distinct digits 1, 2, and 3. See also A035141.
a(14) = 465 as 465 = 3 * 5 * 31 = 253_14 = 3_14 * 5_14 * 23_14, and both 253_14 and its primes factors contain the same distinct digits 2, 3, and 5.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Scott R. Shannon, Apr 29 2024
STATUS
approved