A299403 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 3, and no term occurs twice.

1, 3, 10, 13, 11, 12, 25, 14, 17, 2, 15, 9, 4, 8, 29, 7, 5, 6, 22, 16, 19, 18, 20, 65, 21, 23, 31, 27, 39, 24, 43, 32, 26, 36, 37, 28, 44, 30, 41, 33, 40, 34, 45, 52, 46, 42, 55, 56, 47, 49, 48, 57, 53, 51, 38, 35, 58, 54, 59, 60, 50, 61, 62, 63, 64, 68, 74, 72, 81, 66, 93, 67, 69, 70, 76, 71, 73, 84, 75, 85, 78, 82, 77, 79, 80, 92, 83, 86, 97

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) = 3 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 3 has a digit 3.
a(3) = 10 is the least positive integer not in {1, 3} such that a(3)*a(2) (= 30) has a digit 3: All smaller choices 2, 4, ..., 9 do not satisfy this.
a(4) = 13 is the least positive integer not in {1, 3, 10} such that a(4)*a(3) (= 130) has a digit 3: All smaller choices do not satisfy this.

Prog

(PARI) A299403(n, f=1, d=3, 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. A299402, A298974, ..., A298979: analog with digit 2, 3; ..., 9.

Cf. A299957, A299969, ..., A299988 (analog with addition instead of multiplication, and different digits).

Sequence in context: A044994 A242900 A358266 * A174242 A022415 A344619

Adjacent sequences: A299400 A299401 A299402 * A299404 A299405 A299406

Keyword

nonn,base

Author

M. F. Hasler, Feb 22 2018

Status

approved