OFFSET
0,5
COMMENTS
A binary index of n (row n of A048793) is any position of a 1 in its reversed binary expansion. For example, 18 has reversed binary expansion (0,1,0,0,1) and binary indices {2,5}.
LINKS
John Tyler Rascoe, Table of n, a(n) for n = 0..16384
Wikipedia, Axiom of choice.
EXAMPLE
352 has binary indices of binary indices {{2,3},{1,2,3},{1,4}}, and there are six possible choices (2,1,4), (2,3,1), (2,3,4), (3,1,4), (3,2,1), (3,2,4), so a(352) = 6.
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Length[Select[Tuples[bpe/@bpe[n]], UnsameQ@@#&]], {n, 0, 100}]
PROG
(Python)
from itertools import count, islice, product
def bin_i(n): #binary indices
return([(i+1) for i, x in enumerate(bin(n)[2:][::-1]) if x =='1'])
def a_gen(): #generator of terms
for n in count(0):
c = 0
for j in list(product(*[bin_i(k) for k in bin_i(n)])):
if len(set(j)) == len(j):
c += 1
yield c
A367905_list = list(islice(a_gen(), 90)) # John Tyler Rascoe, May 22 2024
CROSSREFS
Positions of positive terms are A367906.
Positions of zeros are A367907.
Positions of ones are A367908.
Positions of terms > 1 are A367909.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
Cf. A000612, A055621, A072639, A309326, A326031, A326675, A326702, A326753, A367902, A367903, A367904, A367912.
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, Dec 10 2023
STATUS
approved