A298978 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 8, and no term occurs twice.

1, 8, 6, 3, 16, 5, 17, 4, 2, 9, 12, 7, 14, 13, 22, 19, 15, 32, 24, 20, 29, 27, 18, 10, 28, 11, 26, 23, 21, 38, 31, 35, 25, 33, 36, 30, 46, 40, 37, 34, 42, 39, 47, 44, 41, 45, 53, 54, 52, 49, 58, 48, 51, 55, 56, 43, 60, 63, 61, 62, 59, 65, 69, 70, 64, 57, 50, 76, 68, 66, 71, 73, 67, 72, 74, 77, 79, 82, 83, 86, 78, 75, 91, 80, 81, 84, 87, 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) = 8 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 8 has a digit 3.
a(3) = 6 is the least positive integer not in {1, 8} such that a(3)*a(2) (= 48) has a digit 8: All smaller choices 2, 4, ..., 7 do not satisfy this.
a(4) = 3 is the least positive integer not in {1, 6, 8} such that a(4)*a(3) (= 18) has a digit 8: The only smaller choice 2 does not satisfy this.

Prog

(PARI) A298978(n, f=1, d=8, 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, 4, ..., 9.

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

Sequence in context: A154719 A356034 A263181 * A199151 A343275 A177154

Adjacent sequences: A298975 A298976 A298977 * A298979 A298980 A298981

Keyword

nonn,base

Author

M. F. Hasler, Feb 22 2018

Status

approved