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).

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

Author

Rémy Sigrist, Oct 19 2018

Keywords

• nonn
• base

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.

Examples

			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
		

Crossrefs

Cf. A070939, A320674, A320675.

Programs

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