A355791 Numbers that can be written as the product of two divisors greater than 1 such that the number in binary is contained in the string concatenation of the divisors in binary.

6, 10, 12, 14, 24, 28, 30, 36, 42, 48, 56, 57, 60, 62, 96, 112, 120, 124, 126, 136, 170, 192, 224, 240, 248, 252, 254, 292, 355, 384, 448, 480, 496, 504, 508, 510, 528, 682, 737, 768, 896, 921, 960, 992, 1008, 1016, 1020, 1022, 1536, 1792, 1920, 1984, 2016, 2032, 2040, 2044, 2046, 2080, 2184, 2340

Offset

1,1

Links

Table of n, a(n) for n=1..60.

Scott R. Shannon, Divisor product of the first 417 terms. These are all the numbers up to 100000000.

Example

6 is a term as 6 = 110_2 = 3 * 2 = 11_2 * 10_2 and "11" + "10" = "1110" contains "110".
2340 is a term as 2340 = 100100100100_2 = 4 * 585 = 100_2 * 1001001001_2 and "100" + "1001001001" contains "100100100100".
See the attached text file for other examples.

Mathematica

q[n_] := AnyTrue[Rest @ Most @ Divisors[n], StringContainsQ[StringJoin @@ IntegerString[{#, n/#}, 2], IntegerString[n, 2]] &]; Select[Range[2, 2500], q] (* Amiram Eldar, Jul 27 2022 *)

Prog

(Python)
from sympy import divisors
def ok(n):
    b, divs = bin(n)[2:], divisors(n)[1:-1]
    return any(b in bin(d)[2:]+bin(n//d)[2:] for d in divs)
print([k for k in range(1, 2400) if ok(k)]) # Michael S. Branicky, Jul 27 2022

Crossrefs

Cf. A355790 (base-10), A355852, A355857, A030190, A355852, A210959, A027750.

Sequence in context: A028919 A325231 A134620 * A108315 A134616 A362180

Adjacent sequences: A355788 A355789 A355790 * A355792 A355793 A355794

Keyword

nonn,base

Author

Scott R. Shannon, Jul 17 2022

Status

approved