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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][]], 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 May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)