cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A355791 #15 Jul 27 2022 16:36:19
%S A355791 6,10,12,14,24,28,30,36,42,48,56,57,60,62,96,112,120,124,126,136,170,
%T A355791 192,224,240,248,252,254,292,355,384,448,480,496,504,508,510,528,682,
%U A355791 737,768,896,921,960,992,1008,1016,1020,1022,1536,1792,1920,1984,2016,2032,2040,2044,2046,2080,2184,2340
%N 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.
%H A355791 Scott R. Shannon, <a href="/A355791/a355791.txt">Divisor product of the first 417 terms</a>. These are all the numbers up to 100000000.
%e A355791 6 is a term as 6 = 110_2 = 3 * 2 = 11_2 * 10_2 and "11" + "10" = "1110" contains "110".
%e A355791 2340 is a term as 2340 = 100100100100_2 = 4 * 585 = 100_2 * 1001001001_2 and "100" + "1001001001" contains "100100100100".
%e A355791 See the attached text file for other examples.
%t A355791 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 *)
%o A355791 (Python)
%o A355791 from sympy import divisors
%o A355791 def ok(n):
%o A355791     b, divs = bin(n)[2:], divisors(n)[1:-1]
%o A355791     return any(b in bin(d)[2:]+bin(n//d)[2:] for d in divs)
%o A355791 print([k for k in range(1, 2400) if ok(k)]) # _Michael S. Branicky_, Jul 27 2022
%Y A355791 Cf. A355790 (base-10), A355852, A355857, A030190, A355852, A210959, A027750.
%K A355791 nonn,base
%O A355791 1,1
%A A355791 _Scott R. Shannon_, Jul 17 2022