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A307230 Number of divisible pairs of distinct positive integers up to n with at least one binary carry. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 13 22:47 EDT 2021. Contains 343868 sequences. (Running on oeis4.)