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

1,2

Comments

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

Links

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

Example

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)

Mathematica

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

Crossrefs

Cf. A257664, A265740.

Sequence in context: A228380 A090068 A070899 * A332988 A333011 A197562

Adjacent sequences: A265753 A265754 A265755 * A265757 A265758 A265759

Keyword

nonn,base

Author

Hans Havermann, Dec 15 2015

Status

approved