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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, 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.)