OFFSET
1,1
COMMENTS
Decimal digits of m are a permutation of decimal digits of k,
binary digits of m are a permutation of binary digits of k.
Conjecture: there is X such that among integers bigger than X more than 50% are in the sequence.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
1080 and 1800 have the same set of decimal digits, same set of binary digits (10000111000 versus 11100001000), same smallest prime factor 2, and same largest prime factor 5.
MAPLE
Res:= {}:
for n from 1 to 2^16-1 do
f:= numtheory:-factorset(n);
v:= [min(f), max(f), ilog2(n), convert(convert(n, base, 2), `+`), sort(convert(n, base, 10))];
if assigned(R[v]) then
Res:= Res union {n, R[v]}
else
R[v]:= n
fi
od:
sort(convert(Res, list)); # Robert Israel, Sep 28 2018
PROG
(Python)
from collections import defaultdict
from sympy import factorint
def a(up_to):
# up_to should be a power of 2 or 10.
dic = defaultdict(list)
for n in range(2, up_to):
digit_multiset = tuple(sorted(str(n)))
bit_count = n.bit_count()
bit_length = n.bit_length()
factors = factorint(n)
least_prime_factor = min(factors)
greatest_prime_factor = max(factors)
key = (digit_multiset, bit_count, bit_length, least_prime_factor, greatest_prime_factor)
dic[key].append(n)
return sorted(n for n_list in dic.values() if len(n_list) > 1 for n in n_list)
print(*a(2**14), sep=', ')
# David Radcliffe, May 11 2025
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Alex Ratushnyak, Jul 23 2012
STATUS
approved