A299980 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 0, and no term occurs twice.

1, 10, 2, 5, 4, 15, 6, 17, 12, 9, 20, 3, 30, 7, 29, 14, 22, 23, 35, 8, 13, 16, 19, 11, 28, 18, 25, 24, 21, 40, 26, 27, 38, 37, 46, 44, 32, 33, 31, 34, 45, 36, 39, 50, 41, 49, 42, 43, 47, 60, 48, 55, 51, 53, 57, 54, 52, 58, 65, 56, 59, 68, 70, 61, 64, 63, 62, 66, 75, 67, 76, 79, 71, 80, 69, 73, 74, 82, 72, 84, 81, 87, 90, 77, 78, 85, 83, 88, 91

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 0.
a(3) = 2 is the smallest available positive integer, and such that a(3)*a(2) (= 20) has a digit 0.
a(4) = 5 is the least positive integer not in {1, 2, 10} such that a(4)*a(3) (= 10) has a digit 0: The smaller choices 2, 3 and 4 do not satisfy this.

Prog

(PARI) A299980(n, f=1, d=0, 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. A299981, A299402, A299403, A298974, A298975, A299996, A299997, A298978, A298979: analog with digit 1, ..., 9.

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

Sequence in context: A161995 A069036 A155817 * A037922 A111287 A255668

Adjacent sequences: A299977 A299978 A299979 * A299981 A299982 A299983

Keyword

nonn,base

Author

M. F. Hasler, Feb 22 2018

Status

approved