cp's OEIS Frontend

A342130 Decimal numbers m such that the product of the binary string of m and the binary string of m in reverse contains the binary string of m as a substring.

%I A342130 #16 Mar 07 2021 14:46:15
%S A342130 0,1,2,4,8,16,27,32,54,64,108,128,139,165,256,512,815,1024,1630,2048,
%T A342130 2821,3167,3693,3941,4096,4747,5642,6334,7737,7881,8192,9494,10837,
%U A342130 11284,12479,13363,16384,18988,22568,24669,24958,27945,31205,32768,38869,40861,45136,48367,49338,49535,55121
%N A342130 Decimal numbers m such that the product of the binary string of m and the binary string of m in reverse contains the binary string of m as a substring.
%C A342130 All numbers of the form 2^k, k>=0, are in the sequence.
%e A342130 8 is a term as bin(8)*reverse(bin(8)) = 100_2*1_2 = 100_2 contains '100' as a substring.
%e A342130 27 is a term as bin(27)*reverse(bin(27)) = 11011_2*11011_2 = 1011011001_2 contains '11011' as a substring.
%e A342130 108 is a term as bin(108)*reverse(bin(108)) = 1101100_2*11011_2 = 101101100100_2 contains '1101100' as a substring.
%e A342130 139 is a term as bin(139)*reverse(bin(139)) = 10001011_2*11010001_2 = 111000101111011_2 contains '10001011' as a substring.
%o A342130 (PARI) strbin(x) = Str(fromdigits(binary(x), 10));
%o A342130 isok(m) = {my(p = m*fromdigits(Vecrev(binary(m)), 2)); #strsplit(strbin(p), strbin(m)) > 1;} \\ _Michel Marcus_, Mar 01 2021
%Y A342130 Cf. A342127 (base 10), A305989, A007088, A000079, A203565, A332795.
%K A342130 nonn,base
%O A342130 1,3
%A A342130 _Scott R. Shannon_, Mar 01 2021