A299996 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 6, and no term occurs twice.

1, 6, 10, 16, 4, 9, 7, 8, 2, 3, 12, 5, 13, 20, 18, 17, 28, 22, 21, 26, 11, 15, 24, 14, 19, 32, 23, 27, 25, 64, 29, 34, 39, 35, 36, 31, 44, 37, 38, 42, 30, 52, 33, 49, 40, 41, 43, 48, 45, 57, 46, 47, 56, 51, 60, 61, 65, 71, 53, 50, 72, 55, 63, 58, 62, 59, 54, 66, 70, 67, 68, 69, 74, 76, 79, 73, 77, 78, 80, 75, 81, 82, 83, 84, 89, 85, 90, 94, 92

Offset: 1

Author

M. F. Hasler, Feb 22 2018

Keywords

• nonn
• base

Comments

A permutation of the positive integers.

Examples

			a(1) = 1 is the least positive integer, and a(1) has no other constraint to satisfy.
a(2) = 6 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 6 has a digit 6.
a(3) = 10 is the least positive integer not in {1, 6} such that a(3)*a(2) (= 60) has a digit 6: All smaller choices (2, 3, 4 or 5) do not satisfy this.
a(4) = 16 is the least positive integer not in {1, 6, 10} such that a(4)*a(3) (= 160) has a digit 6: All smaller choices 2,...,15 do not satisfy this.
		

Crossrefs

Cf. A299402, A299403, A298974, ..., A298979, A299997: analog with digit 2, 3, ..., 9, 7.

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

Programs

PARI

A299996(n,f=1,d=6,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}