A299981 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 1, and no term occurs twice.

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

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, 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}

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: A262323 A262412 A333722 * A347180 A123895 A147519

Adjacent sequences: A299978 A299979 A299980 * A299982 A299983 A299984

Keyword

nonn,base

Author

M. F. Hasler, Feb 22 2018

Status

approved