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

1,2

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.

Links

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

Example

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}.

Mathematica

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

Prog

(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

Crossrefs

Cf. A008585, A008589, A093140.

Sequence in context: A093764 A194426 A082452 * A049104 A226788 A364718

Adjacent sequences: A362789 A362790 A362791 * A362793 A362794 A362795

Keyword

nonn,base,easy

Author

Alexandru Petrescu, May 04 2023

Status

approved