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A265740 a(1)=1; a(n+1) is the smallest positive integer not yet used such that all the digits of a(n) and a(n+1) are present in the decimal expansion (including any leading and trailing zeros) of a(n)/a(n+1). 3
1, 6, 13, 10, 14, 17, 7, 8, 19, 23, 21, 29, 34, 31, 3, 38, 28, 46, 47, 35, 39, 49, 43, 51, 42, 41, 48, 53, 26, 12, 57, 58, 59, 2, 61, 24, 68, 11, 52, 63, 22, 69, 62, 71, 56, 65, 76, 81, 44, 67, 64, 83, 85, 78, 77, 79, 72, 70, 80, 87, 84, 86, 89, 9, 91, 92, 73 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: a(n) is a permutation of the natural numbers.

The following table shows:

C = number of terms calculated

F = first term that is missing

C           F      F/C

1000        5    0.005

2000       50    0.025

5000     1650    0.330

10000    1650    0.165

20000    2475    0.124

50000   24750    0.495

100000 100000    1.000

200000 199800    0.999

500000 499500    0.999

which seems to support the conjecture.

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..10000

EXAMPLE

   1/6  = 0.1666... (1 and 6 are visible on the right-hand side)

   6/13 = 0.461538461538... (6, 1 and 3 are visible)

  13/10 = 1.30 (trailing zeros are included)

  10/14 = 0.7142857142... (1, 0 and 4)

  14/17 = 0.8235294117... (1, 4 and 7)

  17/7  = 2.4285714285... (1 and 7)

   7/8  = 0.875 (7 and 8)

   ...

MATHEMATICA

f[n_] := Block[{a = {1}, k}, Do[k = If[MissingQ@ #, Max@ a, #] &@ SelectFirst[Range@ Max@ a, ! MemberQ[a, #] &]; While[Or[! AllTrue[Join[IntegerDigits@ a[[i - 1]], IntegerDigits@ k], MemberQ[Union@ Flatten@ Prepend[First@ #, If[Last@ # <= 0, 0, Nothing]] &@ If[Depth@ First@ # < 3, Insert[#, 0, {1, 1}], #] &@ RealDigits[a[[i - 1]]/k], #] &], MemberQ[a, k]], k++]; AppendTo[a, k], {i, 2, n}]; a]; f@ 67 (* Version 10.2 *)

f[n_] := Block[{a = {1}, k}, Do[k = 1; While[Or[If[# == 1, False, True] &[Times @@ Boole[MemberQ[Union@ Flatten@ Prepend[First@ #, If[Last@ # <= 0, 0]] &@ If[Depth@ First@ # < 3, Insert[#, 0, {1, 1}], #] &@ RealDigits[a[[i - 1]]/k], #] & /@ Join[IntegerDigits@ a[[i - 1]], IntegerDigits@ k]]], MemberQ[a, k]], k++]; AppendTo[a, k], {i, 2, n}]; a]; f@ 67 (* Michael De Vlieger, Dec 16 2015, Version 6 *)

CROSSREFS

See A265756 for another version.

See also A257664.

Sequence in context: A229336 A070396 A130012 * A090324 A106623 A115010

Adjacent sequences:  A265737 A265738 A265739 * A265741 A265742 A265743

KEYWORD

nonn,base

AUTHOR

Eric Angelini, submitted by Lars Blomberg, Dec 15 2015

EXTENSIONS

Corrected values for n>=58 by Lars Blomberg, Dec 16 2015

STATUS

approved

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Last modified April 8 21:44 EDT 2020. Contains 333329 sequences. (Running on oeis4.)