A265740 -id:A265740 - cp's OEIS frontend

A265756 a(1)=1; a(n+1) is the smallest positive integer not yet used where all the digits of a(n) and a(n+1) are present in the decimal expansion (excluding any leading or trailing zeros) of a(n)/a(n+1).

1, 6, 13, 17, 7, 8, 14, 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, 87, 80, 89, 9, 86, 92, 73, 27, 84, 93

Offset: 1

Hans Havermann, Dec 15 2015

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

			1/6 = .1666... (1 and 6)
6/13 = .461538461538... (1, 3 and 6)
13/17 = .76470588235294117647058823529411... (1,3 and 7)
Note that term 4 is not 10 because 13/10 = 1.3 (no zero)

Hans Havermann, Table of n, a(n) for n = 1..10000

Cf. A257664, A265740.

t=1; s={1}; Do[c=1; d=IntegerDigits[t]; While[f=Flatten[RealDigits[t/c][[1]]]; u=Union[IntegerDigits[c], d]; Union[Table[MemberQ[f, u[[i]]], {i, Length[u]}]]!={True}||MemberQ[s, c], c++]; t=c; AppendTo[s, t], {400}]; s

A266281 a(1)=1; a(n) is the first integer > a(n-1) with which, in the a(n-1)/a(n) decimal expansion, n is present.

Original entry on oeis.org

1, 4, 11, 13, 14, 17, 19, 22, 23, 29, 34, 47, 58, 61, 65, 87, 89, 93, 94, 97, 102, 103, 105, 109, 113, 115, 116, 118, 121, 130, 131, 136, 139, 141, 149, 152, 157, 159, 161, 166, 167, 169, 174, 177, 179, 181, 184, 188, 191, 193, 194, 197, 199, 203, 218, 223, 224

Offset: 1

Francesco Di Matteo, Dec 26 2015

Two other sequences are possible without the a(n)>a(n-1) limitation, one with a(n) terms already used in the sequences (where the n growth does not allow data looping), another only with a(n) terms not yet used.

			a(8) = 22 because a(7) = 19 and "8" does not appear in the digital expansion of 19/20 = 0.95 nor of 19/21 = 0.904761904761..., but it does appear in 19/22 = 0.86363...;
a(9) = 23 because 22/23 = 0.9565217391304..., where "9" does appear;
a(10) = 29 because "10" does not appear in the digital expansion of 23/k for k=24..28, but it does appear in 23/29 = 0.7931034...

Francesco Di Matteo, Table of n, a(n) for n = 1..1000

Cf. A257664, A265740, A265756.

f[n_] := Block[{a = {1}, k}, Do[k = a[[m - 1]] + 1; While[SequenceCount[Flatten@ First@ RealDigits[a[[m - 1]]/k], IntegerDigits@ m] < 1, k++]; AppendTo[a, k], {m, 2, n}]; a]; f@ 57 (* Version 10.1, or *)
f[n_] := Block[{a = {1}, k}, Do[k = a[[m - 1]] + 1; While[StringCount[
ToString[FromDigits@ Flatten@ First@ RealDigits[a[[m - 1]]/k]], ToString@ m] < 1, k++]; AppendTo[a, k], {m, 2, n}]; a]; f@ 57 (* Michael De Vlieger, Dec 30 2015, Version 5.1 *)

cp's OEIS Frontend

A265756 a(1)=1; a(n+1) is the smallest positive integer not yet used where all the digits of a(n) and a(n+1) are present in the decimal expansion (excluding any leading or trailing zeros) of a(n)/a(n+1).

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