A307230 Number of divisible pairs of distinct positive integers up to n with at least one binary carry.

0, 0, 0, 1, 1, 2, 4, 5, 5, 7, 8, 9, 11, 12, 14, 17, 17, 18, 21, 22, 24, 27, 29, 30, 32, 34, 36, 39, 42, 43, 49, 50, 50, 53, 54, 57, 60, 61, 63, 66, 68, 69, 74, 75, 78, 83, 85, 86, 88, 90, 93, 96, 99, 100, 105, 108, 111, 114, 116, 117, 125, 126, 128, 133, 133

Offset

0,6

Comments

Two positive integers are divisible if the first divides the second, and have a binary carry if the positions of 1's in their reversed binary expansion overlap.

Links

Table of n, a(n) for n=0..64.

Formula

a(n) = A325124(n) - n.

Example

The a(3) = 1 through a(12) = 11 pairs:
  {1,3}  {1,3}  {1,3}  {1,3}  {1,3}  {1,3}  {1,3}  {1,3}   {1,3}   {1,3}
                {1,5}  {1,5}  {1,5}  {1,5}  {1,5}  {1,5}   {1,5}   {1,5}
                       {2,6}  {1,7}  {1,7}  {1,7}  {1,7}   {1,7}   {1,7}
                       {3,6}  {2,6}  {2,6}  {1,9}  {1,9}   {1,9}   {1,9}
                              {3,6}  {3,6}  {2,6}  {2,6}   {2,6}   {2,6}
                                            {3,6}  {3,6}   {3,6}   {3,6}
                                            {3,9}  {3,9}   {3,9}   {3,9}
                                                   {2,10}  {1,11}  {1,11}
                                                           {2,10}  {2,10}
                                                                   {4,12}
                                                                   {6,12}

Mathematica

Table[Length[Select[Subsets[Range[n], {2}], Divisible@@Reverse[#]&&Intersection[Position[Reverse[IntegerDigits[#[[1]], 2]], 1], Position[Reverse[IntegerDigits[#[[2]], 2]], 1]]!={}&]], {n, 0, 20}]

Crossrefs

Cf. A006218, A019565, A050315, A070939, A080572, A247935, A267610.

Cf. A325095, A325096, A325101, A325103, A325104, A325105, A325106, A325124.

Sequence in context: A278480 A260489 A140202 * A026404 A327326 A170882

Adjacent sequences: A307227 A307228 A307229 * A307231 A307232 A307233

Keyword

nonn

Author

Gus Wiseman, Mar 29 2019

Status

approved