OFFSET
0,3
COMMENTS
Two positive integers are divisible if the first divides the second, and they have a binary carry if the positions of 1's in their reversed binary expansion overlap.
FORMULA
a(n) = A307230(n) + n.
EXAMPLE
The a(1) = 1 through a(8) = 13 pairs:
(1,1) (1,1) (1,1) (1,1) (1,1) (1,1) (1,1) (1,1)
(2,2) (1,3) (1,3) (1,3) (1,3) (1,3) (1,3)
(2,2) (2,2) (1,5) (1,5) (1,5) (1,5)
(3,3) (3,3) (2,2) (2,2) (1,7) (1,7)
(4,4) (3,3) (2,6) (2,2) (2,2)
(4,4) (3,3) (2,6) (2,6)
(5,5) (3,6) (3,3) (3,3)
(4,4) (3,6) (3,6)
(5,5) (4,4) (4,4)
(6,6) (5,5) (5,5)
(6,6) (6,6)
(7,7) (7,7)
(8,8)
MATHEMATICA
Table[Length[Select[Tuples[Range[n], 2], Divisible@@Reverse[#]&&Intersection[Position[Reverse[IntegerDigits[#[[1]], 2]], 1], Position[Reverse[IntegerDigits[#[[2]], 2]], 1]]!={}&]], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 29 2019
STATUS
approved