

A299980


Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 0, and no term occurs twice.


8



1, 10, 2, 5, 4, 15, 6, 17, 12, 9, 20, 3, 30, 7, 29, 14, 22, 23, 35, 8, 13, 16, 19, 11, 28, 18, 25, 24, 21, 40, 26, 27, 38, 37, 46, 44, 32, 33, 31, 34, 45, 36, 39, 50, 41, 49, 42, 43, 47, 60, 48, 55, 51, 53, 57, 54, 52, 58, 65, 56, 59, 68, 70, 61, 64, 63, 62, 66, 75, 67, 76, 79, 71, 80, 69, 73, 74, 82, 72, 84, 81, 87, 90, 77, 78, 85, 83, 88, 91
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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) = 10 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 10 has a digit 0.
a(3) = 2 is the smallest available positive integer, and such that a(3)*a(2) (= 20) has a digit 0.
a(4) = 5 is the least positive integer not in {1, 2, 10} such that a(4)*a(3) (= 10) has a digit 0: The smaller choices 2, 3 and 4 do not satisfy this.


PROG

(PARI) A299980(n, f=1, d=0, 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. A299981, A299402, A299403, A298974, A298975, A299996, A299997, A298978, A298979: analog with digit 1, ..., 9.
Cf. A299957, A299969, ..., A299988: analog with addition instead of multiplication, and different digits.
Sequence in context: A161995 A069036 A155817 * A037922 A111287 A255668
Adjacent sequences: A299977 A299978 A299979 * A299981 A299982 A299983


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Feb 22 2018


STATUS

approved



