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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). 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 20 12:50 EST 2019. Contains 319330 sequences. (Running on oeis4.)