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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
OFFSET
1,2
COMMENTS
Positive powers of ten (A011557) and pandigital numbers (A050289 and A171102) will never appear.
Is the sequence finite?
LINKS
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
KEYWORD
nonn,base
AUTHOR
Eric Angelini and Hans Havermann, Jul 12 2015
STATUS
approved