A257664 a(1)=1; a(n+1) is the smallest positive integer not yet used where the digits of the decimal expansion (disregarding all leading and trailing zeros) of a(n)/a(n+1) have no digit in common with either a(n) or a(n+1).

1, 2, 3, 4, 5, 6, 8, 11, 15, 25, 22, 20, 24, 27, 9, 12, 16, 32, 33, 30, 40, 18, 36, 44, 37, 45, 50, 60, 48, 64, 72, 54, 55, 66, 73, 77, 7, 14, 21, 28, 42, 70, 35, 75, 82, 110, 41, 108, 111, 125, 132, 135, 150, 225, 202, 220, 200, 240, 80, 120, 128, 192, 216, 243, 270

Offset

1,2

Comments

Positive powers of ten (A011557) and pandigital numbers (A050289 and A171102) will never appear.

Is the sequence finite?

Links

Hans Havermann, Table of n, a(n) for n = 1..2000

Eric Angelini, Division with no visible digits, SeqFan list, July 9, 2015.

Example

a(2) is 2 because it is the smallest number not yet used where the digits of a(1)/a(2) = .5, i.e., 5, is neither 1 nor 2.
a(3) is 3 because it is the smallest number not yet used where the digits of a(2)/a(3) = .666.., i.e., 6, is neither 2 nor 3.
a(4) is 4 because it is the smallest number not yet used where the digits of a(3)/a(4) = .75, i.e., 5 and 7, are neither 3 nor 4.
a(72) is 63 because it is the smallest number not yet used where the digits of a(71)/a(72) = 90/63 = 1.42857142857.., i.e., 1, 2, 4, 5, 7, and 8, are not any of 0, 3, 6, or 9.
a(376) is 15000 because it is the smallest number not yet used where the digits of a(375)/a(376) = 1025/15000 = .068333.., i.e., 3, 6, and 8 (the zero is leading) are not any of 0, 1, 2, or 5.

Mathematica

t = 1; s = {1}; Do[c = 1; d = IntegerDigits[t]; While[Intersection[Flatten[RealDigits[t/c][[1]]], Join[IntegerDigits[c], d]] != {} || MemberQ[s, c], c++]; t = c; AppendTo[s, t], {400}]; s

Crossrefs

Sequence in context: A322340 A282504 A022468 * A181324 A050933 A103302

Adjacent sequences: A257661 A257662 A257663 * A257665 A257666 A257667

Keyword

nonn,base

Author

Eric Angelini and Hans Havermann, Jul 12 2015

Status

approved