

A298979


Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 9, and no term occurs twice.


15



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

1,2


COMMENTS

A permutation of the positive integers.


LINKS

Table of n, a(n) for n=1..89.


EXAMPLE

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.


PROG

(PARI) A298979(n, f=1, d=9, a=1, u=[a])={for(n=2, n, f&&if(f==1, print1(a", "), write(f, n1, " "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}


CROSSREFS

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).
Sequence in context: A260042 A141640 A231504 * A299969 A050551 A022099
Adjacent sequences: A298976 A298977 A298978 * A298980 A298981 A298982


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Feb 22 2018


STATUS

approved



