

A161156


Positive integers n such that {the number of (nonleading) 0's in the binary representation of n} is coprime to n, and {the number of 1's in the binary representation of n} is coprime to n, but {the number of digits in the binary representation of n} is not coprime to n.


5



2, 8, 14, 25, 32, 33, 38, 39, 44, 45, 50, 51, 52, 56, 57, 62, 77, 91, 119, 128, 134, 146, 148, 152, 158, 164, 176, 182, 188, 194, 196, 206, 208, 214, 218, 224, 236, 242, 244, 248, 254, 267, 279, 291, 297, 309, 327, 333, 339, 351, 357, 369, 375, 381, 387, 393
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OFFSET

1,1


COMMENTS

1 is the only integer of the form 2^k 1 (k>=0) which is coprime to the number of 0's in its binary representation, 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[393], 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, 393, 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, A161155.
Sequence in context: A121055 A107072 A120413 * A125902 A295055 A277276
Adjacent sequences: A161153 A161154 A161155 * A161157 A161158 A161159


KEYWORD

base,nonn


AUTHOR

Leroy Quet, Jun 03 2009


EXTENSIONS

Extended by Ray Chandler, Jun 11 2009


STATUS

approved



