A299997 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 7, and no term occurs twice.

1, 7, 10, 17, 11, 16, 36, 2, 35, 5, 14, 27, 21, 13, 6, 12, 23, 9, 3, 19, 4, 18, 15, 25, 28, 24, 30, 26, 22, 8, 34, 50, 54, 31, 37, 20, 38, 44, 29, 33, 39, 43, 32, 46, 45, 55, 65, 42, 41, 47, 51, 53, 49, 56, 62, 48, 57, 61, 52, 63, 59, 64, 58, 72, 66, 83, 69, 40, 68, 70, 71, 67, 81, 75, 73, 79, 60, 95, 74, 78, 86, 82, 85, 84, 80, 88, 77, 91, 87

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) = 7 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 7 has a digit 7.
a(3) = 10 is the least positive integer not in {1, 7} such that a(3)*a(2) (= 70) has a digit 7: All smaller choices (2, ..., 6) do not satisfy this.
a(4) = 17 is the least positive integer not in {1, 7, 10} such that a(4)*a(3) (= 170) has a digit 7: All smaller choices 2,...,16 do not satisfy this.

Prog

(PARI) A299997(n, f=1, d=7, 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, A299996: analog with digit 2, 3, 4, ..., 9, 6.

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

Sequence in context: A286873 A218128 A175666 * A299987 A192273 A098748

Adjacent sequences: A299994 A299995 A299996 * A299998 A299999 A300000

Keyword

nonn,base

Author

M. F. Hasler, Feb 22 2018

Status

approved