A298975 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 5, and no term occurs twice.

1, 5, 3, 15, 7, 8, 19, 24, 21, 12, 13, 4, 14, 11, 23, 22, 16, 32, 17, 9, 6, 25, 2, 26, 20, 27, 28, 18, 29, 33, 35, 10, 45, 30, 50, 31, 34, 37, 41, 38, 40, 39, 55, 43, 36, 42, 49, 44, 57, 62, 46, 56, 51, 52, 53, 48, 47, 54, 64, 68, 67, 59, 60, 75, 58, 61, 65, 63, 66, 69, 73, 70, 72, 71, 74, 76, 77, 85, 79, 83, 91, 94, 80, 82, 86, 88, 87, 95, 81

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) = 5 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 5 has a digit 5.
a(3) = 3 is the least positive integer not in {1, 5} such that a(3)*a(2) (= 15) has a digit 5: The smaller choice 2 does not satisfy this.
a(4) = 15 is the least positive integer not in {1, 3, 5} such that a(4)*a(3) (= 75) has a digit 5: All available smaller choices do not satisfy this.

Prog

(PARI) A298975(n, f=1, d=5, 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: analog with digit 2, 3; ..., 9.

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

Sequence in context: A351951 A329029 A248983 * A070375 A166465 A162813

Adjacent sequences: A298972 A298973 A298974 * A298976 A298977 A298978

Keyword

nonn,base

Author

M. F. Hasler, Feb 22 2018

Status

approved