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A298975
Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 5, and no term occurs twice.
10
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.
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
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Feb 22 2018
STATUS
approved