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A299403
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Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 3, and no term occurs twice.
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14
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1, 3, 10, 13, 11, 12, 25, 14, 17, 2, 15, 9, 4, 8, 29, 7, 5, 6, 22, 16, 19, 18, 20, 65, 21, 23, 31, 27, 39, 24, 43, 32, 26, 36, 37, 28, 44, 30, 41, 33, 40, 34, 45, 52, 46, 42, 55, 56, 47, 49, 48, 57, 53, 51, 38, 35, 58, 54, 59, 60, 50, 61, 62, 63, 64, 68, 74, 72, 81, 66, 93, 67, 69, 70, 76, 71, 73, 84, 75, 85, 78, 82, 77, 79, 80, 92, 83, 86, 97
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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) = 3 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 3 has a digit 3.
a(3) = 10 is the least positive integer not in {1, 3} such that a(3)*a(2) (= 30) has a digit 3: All smaller choices 2, 4, ..., 9 do not satisfy this.
a(4) = 13 is the least positive integer not in {1, 3, 10} such that a(4)*a(3) (= 130) has a digit 3: All smaller choices do not satisfy this.
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PROG
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(PARI) A299403(n, f=1, d=3, 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. 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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