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A161155
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Positive integers n such that {the number of (non-leading) 0's in the binary representation of n} is coprime to n, {the number of 1's in the binary representation of n} is coprime to n and {the number of digits in the binary representation of n} is coprime to n.
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5
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1, 5, 9, 11, 13, 17, 19, 23, 27, 29, 35, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 85, 87, 89, 93, 95, 97, 101, 103, 107, 109, 113, 117, 121, 125, 131, 133, 135, 137, 139, 141, 143, 147, 149, 151, 153, 157, 161, 163, 165, 167, 169, 173, 175, 177, 179, 181
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OFFSET
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1,2
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COMMENTS
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1 is the only integer of the form 2^k -1 (k>=0) included in this sequence, because such integers contain no binary 0's, and 0 is considered here to be coprime only to 1.
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LINKS
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MATHEMATICA
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Select[Range[181], GCD[DigitCount[#, 2, 0] , #]==1 && GCD[DigitCount[#, 2, 1], #]==1 && GCD[Length[IntegerDigits[#, 2]], #]==1 &] (* Indranil Ghosh, Mar 08 2017 *)
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PROG
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(PARI) b0(n) = if(n<1, 0, b0(n\2) + 1 - n%2);
b1(n) = if(n<1, 0, b1(n\2) + n%2);
for (n=1, 181, if(gcd(b0(n), n) == 1 && gcd(b1(n), n) == 1 && gcd(#digits(n, 2), n) == 1, print1(n", "))) \\ Indranil Ghosh, Mar 08 2017
(Python)
from fractions import gcd
i=j=1
while j<=100:
if gcd(bin(i)[2:].count("0"), i)==1 and gcd(bin(i)[2:].count("1"), i)==1 and gcd(len(bin(i)[2:]), i)==1:
print(str(j)+" "+str(i))
j+=1
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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