A320673 - OEIS

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

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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.

LINKS

Table of n, a(n) for n=1..27.

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

Cf. A070939, A320674, A320675.

Sequence in context: A134691 A139182 A294297 * A081646 A215908 A052261

Adjacent sequences: A320670 A320671 A320672 * A320674 A320675 A320676

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Oct 19 2018

STATUS

approved