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

1,2

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) = 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.

Prog

(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}

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).

Sequence in context: A117309 A228300 A342480 * A315289 A108936 A315290

Adjacent sequences: A299993 A299994 A299995 * A299997 A299998 A299999

Keyword

nonn,base

Author

M. F. Hasler, Feb 22 2018

Status

approved