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A065609
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Positive m such that when written in binary, no rotated value of m is greater than m.
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38
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1, 2, 3, 4, 6, 7, 8, 10, 12, 14, 15, 16, 20, 24, 26, 28, 30, 31, 32, 36, 40, 42, 48, 50, 52, 54, 56, 58, 60, 62, 63, 64, 72, 80, 84, 96, 98, 100, 104, 106, 108, 112, 114, 116, 118, 120, 122, 124, 126, 127, 128, 136, 144, 160, 164, 168, 170, 192, 194, 196, 200, 202
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Rotated values of m are defined as the numbers which occur when m is shifted 1, 2, ... bits to the right with the last bits added to the front; e.g., the rotated values of 1011 are 1011, 1101, 1110 and 0111.
The number of k-bit binary numbers in this sequence is A008965. This gives the row lengths when the sequence is regarded as a table.
If m is in the sequence, then so is 2m. All odd terms are of the form 2^k - 1. - Ivan Neretin, Aug 04 2016
First differs from A328595 in lacking 44, with binary expansion {1, 0, 1, 1, 0, 0}, and 92, with binary expansion {1, 0, 1, 1, 1, 0, 0}. - Gus Wiseman, Oct 31 2019
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LINKS
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EXAMPLE
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14 is included because 14 in binary is 1110. 1110 has the rotated values of 0111, 1011 and 1101 -- 7, 11 and 13 -- which are all smaller than 14.
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MAPLE
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filter:= proc(n) local L, k;
if n::odd then return evalb(n+1 = 2^ilog2(n+1)) fi;
L:= convert(convert(n, binary), string);
for k from 1 to length(L)-1 do
if not lexorder(StringTools:-Rotate(L, k), L) then return false fi;
od;
true
end proc:
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MATHEMATICA
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Select[Range[200], # == Max[FromDigits[#, 2] & /@ NestList[RotateLeft, dg = IntegerDigits[#, 2], Length@dg]] &] (* Ivan Neretin, Aug 04 2016 *)
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PROG
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(Python)
def ok(n):
b = bin(n)[2:]
return b > "0" and all(b[i:] + b[:i] <= b for i in range(1, len(b)))
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CROSSREFS
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The version with the most significant digit ignored is A328668 or A328607.
Numbers whose reversed binary expansion is a Lyndon word are A328596.
Numbers whose binary expansion is aperiodic are A328594.
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KEYWORD
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base,nonn,tabf
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AUTHOR
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Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Nov 06 2001
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EXTENSIONS
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STATUS
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approved
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