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A161155 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. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..1000

MATHEMATICA

Select[Range[181], GCD[DigitCount[#, 2, 0] , #]==1 && GCD[DigitCount[#, 2, 1], #]==1 && GCD[Length[IntegerDigits[#, 2]], #]==1 &] (* Indranil Ghosh, Mar 08 2017 *)

PROG

(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<=1000:

....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

....i+=1 # Indranil Ghosh, Mar 08 2017

CROSSREFS

Cf. A094387, A161152, A161153, A161154, A161156.

Sequence in context: A043757 A043766 A063479 * A314585 A078621 A287521

Adjacent sequences:  A161152 A161153 A161154 * A161156 A161157 A161158

KEYWORD

base,nonn

AUTHOR

Leroy Quet, Jun 03 2009

EXTENSIONS

Extended by Ray Chandler, Jun 11 2009

STATUS

approved

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Last modified August 21 05:37 EDT 2019. Contains 326162 sequences. (Running on oeis4.)