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A298974
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Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 4, and no term occurs twice.
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15
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1, 4, 6, 7, 2, 12, 17, 20, 21, 14, 3, 8, 5, 9, 16, 15, 23, 18, 13, 11, 22, 19, 24, 10, 34, 26, 29, 36, 39, 32, 27, 35, 40, 31, 37, 38, 28, 30, 47, 42, 44, 33, 43, 48, 50, 49, 46, 51, 54, 41, 45, 52, 57, 25, 56, 58, 53, 65, 62, 55, 59, 60, 64, 61, 63, 66, 67, 68, 69, 70, 71, 74, 73, 75, 72, 76, 79, 82, 77, 84, 81, 80, 78, 83, 88, 85, 97, 86, 87
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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) = 4 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 4 has a digit 4.
a(3) = 6 is the least positive integer not in {1, 4} such that a(3)*a(2) (= 24) has a digit 4: The smaller choices 2, 3 and 5 do not satisfy this.
a(4) = 7 is the least positive integer not in {1, 4, 6} such that a(4)*a(3) (= 42) has a digit 4: All available smaller choices do not satisfy this.
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PROG
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(PARI) A298974(n, f=1, d=4, 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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