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A320673
Positive integers m with binary expansion (b_1, ..., b_k) (where k = A070939(m)) such that b_i = [m == 0 (mod i)] for i = 1..k (where [] is an Iverson bracket).
3
1, 50, 52, 104, 114, 3460, 12298, 29442, 31368, 856592, 1713184, 54822416, 109578256, 109644832, 219156512, 219289664, 438313024, 438579328, 876626048, 877158656, 1034367516, 1753252096, 1754317312, 112208117792, 113290248736, 224416235584, 226580497472
OFFSET
1,2
COMMENTS
In other words, the binary representation of a term of this sequence encodes the first divisors and nondivisors of this term respectively as ones and zeros.
Is this sequence infinite?
See A320674 and A320675 for similar sequences.
EXAMPLE
The first terms, alongside their binary representation and the divisors encoded therein, are:
n a(n) bin(a(n)) First divisors
- ----- --------------- --------------------
1 1 1 1
2 50 110010 1, 2, 5
3 52 110100 1, 2, 4
4 104 1101000 1, 2, 4
5 114 1110010 1, 2, 3, 6
6 3460 110110000100 1, 2, 4, 5, 10
7 12298 11000000001010 1, 2, 11, 13
8 29442 111001100000010 1, 2, 3, 6, 7, 14
9 31368 111101010001000 1, 2, 3, 4, 6, 8, 12
PROG
(PARI) is(n) = my (b=binary(n)); b==vector(#b, k, n%k==0)
(Python)
from itertools import count, islice
def A320673_gen(startvalue=0): # generator of terms >= startvalue
return filter(lambda n:not any(int(b)==bool(n%i) for i, b in enumerate(bin(n)[2:], 1)), count(max(startvalue, 0)))
A320673_list = list(islice(A320673_gen(), 10)) # Chai Wah Wu, Dec 12 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Oct 19 2018
STATUS
approved