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.

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

Scott R. Shannon, Table of n, a(n) for n = 2..404

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

Cf. A027746, A035141, A035140, A372309, A371695, A000668.

Sequence in context: A297638 A256456 A270522 * A317583 A020331 A248476

Adjacent sequences: A372381 A372382 A372383 * A372385 A372386 A372387

Keyword

nonn,base

Author

Scott R. Shannon, Apr 29 2024

Status

approved