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A298979
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Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 9, and no term occurs twice.
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15
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1, 9, 10, 19, 5, 18, 11, 27, 7, 13, 3, 23, 4, 24, 8, 12, 16, 6, 15, 26, 35, 14, 21, 29, 17, 37, 25, 36, 22, 41, 34, 28, 32, 30, 31, 39, 46, 2, 45, 20, 47, 42, 38, 50, 58, 33, 43, 44, 59, 49, 40, 48, 52, 56, 53, 55, 54, 61, 64, 62, 63, 57, 51, 69, 68, 72, 82, 60, 65, 66, 75, 79, 67, 70, 71, 76, 78, 73, 81, 74, 77, 83, 84, 88, 90, 91, 87, 80, 99
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OFFSET
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1,2
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COMMENTS
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A permutation of the positive integers.
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LINKS
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EXAMPLE
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a(1) = 1 is the least positive integer, and a(1) has no other constraint to satisfy.
a(2) = 9 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 9 has a digit 9.
a(3) = 10 is the least positive integer not in {1, 9} such that a(3)*a(2) (= 90) has a digit 9: The smaller choices 2, ..., 8 does not satisfy this.
a(4) = 19 is the least positive integer not in {1, 9, 10} such that a(4)*a(3) (= 190) has a digit 5: All available smaller choices do not satisfy this.
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PROG
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(PARI) A298979(n, f=1, d=9, a=1, u=[a])={for(n=2, n, f&&if(f==1, print1(a", "), write(f, n-1, " "a)); for(k=u[1]+1, oo, setsearch(u, k)&&next; setsearch(Set(digits(a*k)), d)&&(a=k)&&break); u=setunion(u, [a]); while(#u>1&&u[2]==u[1]+1, u=u[^1])); a}
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CROSSREFS
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Cf. A299980, A299981, A299402, A299403, A298974, A298975, A299996, A299997, A298978 : analog with digit 0, 1,..., 8.
Cf. A299957, A299969, ..., A299988 (analog with addition instead of multiplication, and different digits).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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