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.

0, 1, 2, 4, 8, 16, 27, 32, 54, 64, 108, 128, 139, 165, 256, 512, 815, 1024, 1630, 2048, 2821, 3167, 3693, 3941, 4096, 4747, 5642, 6334, 7737, 7881, 8192, 9494, 10837, 11284, 12479, 13363, 16384, 18988, 22568, 24669, 24958, 27945, 31205, 32768, 38869, 40861, 45136, 48367, 49338, 49535, 55121

Offset: 1

Author

Scott R. Shannon, Mar 01 2021

Keywords

• nonn
• base

Comments

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

Examples

			8 is a term as bin(8)*reverse(bin(8)) = 100_2*1_2 = 100_2 contains '100' as a substring.
27 is a term as bin(27)*reverse(bin(27)) = 11011_2*11011_2 = 1011011001_2 contains '11011' as a substring.
108 is a term as bin(108)*reverse(bin(108)) = 1101100_2*11011_2 = 101101100100_2 contains '1101100' as a substring.
139 is a term as bin(139)*reverse(bin(139)) = 10001011_2*11010001_2 = 111000101111011_2 contains '10001011' as a substring.
		

Crossrefs

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

Programs

PARI

strbin(x) = Str(fromdigits(binary(x), 10));
isok(m) = {my(p = m*fromdigits(Vecrev(binary(m)), 2)); #strsplit(strbin(p), strbin(m)) > 1;} \\ Michel Marcus, Mar 01 2021