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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.
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%I #16 Mar 07 2021 14:46:15

%S 0,1,2,4,8,16,27,32,54,64,108,128,139,165,256,512,815,1024,1630,2048,

%T 2821,3167,3693,3941,4096,4747,5642,6334,7737,7881,8192,9494,10837,

%U 11284,12479,13363,16384,18988,22568,24669,24958,27945,31205,32768,38869,40861,45136,48367,49338,49535,55121

%N 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 All numbers of the form 2^k, k>=0, are in the sequence.

%e 8 is a term as bin(8)*reverse(bin(8)) = 100_2*1_2 = 100_2 contains '100' as a substring.

%e 27 is a term as bin(27)*reverse(bin(27)) = 11011_2*11011_2 = 1011011001_2 contains '11011' as a substring.

%e 108 is a term as bin(108)*reverse(bin(108)) = 1101100_2*11011_2 = 101101100100_2 contains '1101100' as a substring.

%e 139 is a term as bin(139)*reverse(bin(139)) = 10001011_2*11010001_2 = 111000101111011_2 contains '10001011' as a substring.

%o (PARI) strbin(x) = Str(fromdigits(binary(x), 10));

%o isok(m) = {my(p = m*fromdigits(Vecrev(binary(m)), 2)); #strsplit(strbin(p), strbin(m)) > 1;} \\ _Michel Marcus_, Mar 01 2021

%Y Cf. A342127 (base 10), A305989, A007088, A000079, A203565, A332795.

%K nonn,base

%O 1,3

%A _Scott R. Shannon_, Mar 01 2021