A342242 For any n > 0, a(n) is the least positive number whose binary expansion is both a prefix and a suffix of the binary expansion of n; a(0) = 0.
0, 1, 2, 1, 4, 1, 6, 1, 8, 1, 2, 1, 12, 1, 14, 1, 16, 1, 2, 1, 20, 1, 2, 1, 24, 1, 26, 1, 28, 1, 30, 1, 32, 1, 2, 1, 4, 1, 2, 1, 40, 1, 2, 1, 44, 1, 2, 1, 48, 1, 50, 1, 52, 1, 6, 1, 56, 1, 58, 1, 60, 1, 62, 1, 64, 1, 2, 1, 4, 1, 2, 1, 72, 1, 2, 1, 4, 1, 2, 1
Offset: 0
Examples
For n = 814: - the binary expansion of 814 is "1100101110", - "1" does not match "0", - "11" does not match "10", - "110" matches "110", - so the binary representation of a(814) is "110", - and a(814) = 6.
Links
Programs
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PARI
a(n) = { my (b=if (n, binary(n), [0])); for (w=1, oo, if (b[1..w]==b[#b+1-w..#b], return (fromdigits(b[1..w],2)))) } -
Python
def a(n): b = bin(n)[2:] for i in range(1, len(b)+1): if b[:i] == b[-i:]: return int(b[:i], 2) print([a(n) for n in range(80)]) # Michael S. Branicky, Mar 07 2021
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