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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.)