

A299981


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


8



1, 10, 11, 12, 9, 2, 5, 3, 4, 25, 6, 17, 7, 13, 8, 14, 15, 21, 31, 23, 18, 34, 24, 38, 27, 19, 22, 28, 29, 35, 26, 16, 32, 33, 36, 30, 37, 39, 40, 41, 42, 43, 44, 45, 47, 46, 59, 20, 50, 62, 51, 61, 52, 56, 57, 53, 55, 58, 54, 65, 48, 66, 63, 67, 73, 70, 74, 69, 49, 64, 80, 77, 82, 75, 68, 76, 81, 71, 72, 78, 79, 85, 60, 86, 83, 87, 91, 90, 89
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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 1. (For all small choices 2, ..., 9 this is not the case.)
a(3) = 11 is the smallest positive integer not in {1, 10} such that a(3)*a(2) (= 110) has a digit 1.
a(4) = 12 is the least positive integer not in {1, 10, 11} such that a(4)*a(3) (= 132) has a digit 1: All smaller choices 2, 3, ..., 9 do not satisfy this.


PROG

(PARI) A299981(n, f=1, d=1, 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, A299402, A299403, A298974, A298975, A299996, A299997, A298978, A298979: analog with digit 0, 2, ..., 9.
Cf. A299957, A299969, ..., A299988: analog with addition instead of multiplication, and different digits.
Sequence in context: A286890 A262323 A262412 * A123895 A147519 A303657
Adjacent sequences: A299978 A299979 A299980 * A299982 A299983 A299984


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Feb 22 2018


STATUS

approved



