OFFSET
1,1
COMMENTS
This sequence is the intersection of sets A010061 and A055938, where: set A010061 is NONE of ( k + count of set binary bits(k) ), and set A055938 is NONE of ( k - count of set binary bits(k) ), for any k.
The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 1, 9, 127, 1362, 12921, 128429, 1261747, 12554142, 125697648, 1257065977, ... . Conjecture: This sequence has an asymptotic density (1/2) * A242403 = 0.126330... . - Amiram Eldar, Oct 02 2022
LINKS
Andres M. Torres, Table of n, a(n) for n = 1..1000
Andres M. Torres, Zip file containing Blitz3D code.
EXAMPLE
Find the list of values not defined by:
V = i +- count of set binary bits(i), for any integer i.
Assume that setbits(n) returns the count of set binary digits of n.
A227359 sample: 6,13,21,30,37,48,51,80,83,111, ...
0 +- setbits(0) = 0 therefore 0 does not make the list
1 +- setbits(1) = 0,2 therefore 0 and 2 do not make the list
2 +- setbits(2) = 1,3 therefore 1 and 3 do not make the list
3 +- setbits(3) = 1,5 therefore 1 and 5 do not make the list
4 +- setbits(4) = 3,5 ...
5 +- setbits(5) = 3,7 therefore 3 and 7 do not make the list
6 +- setbits(6) = 4,8 therefore 4 and 8 do not make the list
7 +- setbits(7) = 4,10 therefore 4 and 10 do not make the list
8 +- setbits(8) = 7,9 therefore 7 and 9 do not make the list
6 and 13 did make the list because there is no solution for
6 = i +- setbits(i), nor
13 = i +- setbits(i), for any integer i.
PROG
See link.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Andres M. Torres, Jul 08 2013
STATUS
approved