A362792 Numbers k such that 3*k and 7*k share the same set of digits.

0, 45, 75, 423, 445, 450, 513, 750, 891, 1089, 1305, 2382, 2497, 4230, 4445, 4450, 4488, 4491, 4500, 4505, 4513, 4878, 5013, 5045, 5130, 5133, 5868, 7317, 7500, 7686, 8360, 8703, 8891, 8901, 8910, 8911, 8955, 8991, 9756, 9891, 10089, 10449, 10889, 10890, 10891

Offset: 1

Author

Alexandru Petrescu, May 04 2023

Keywords

• nonn
• base
• easy

Comments

The sequence is infinite because if k is a term, then 10*k is also a term.

Every number k of the form 44...45 (one of more 4's followed by 5, cf. A093140) is a term because 3*k = 133...35 and 7*k = 311...15.

Examples

			k = 75 is a term because 3*k = 225 and 7*k = 525 share the same set of digits, namely {2,5}.
k = 423 is a term because 3*k = 1269 and 7*k = 2961 share the same set of digits, namely {1,2,6,9}.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008585, A008589, A093140.

Programs

Mathematica

Select[Range[0, 11000], Union[IntegerDigits[3*#]] == Union[IntegerDigits[7*#]] &] (* Amiram Eldar, May 18 2023 *)

PARI

isok(k) = Set(digits(3*k)) == Set(digits(7*k));

Python

def ok(n): return set(str(3*n)) == set(str(7*n))
print([k for k in range(11000) if ok(k)]) # Michael S. Branicky, May 04 2023