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%I #6 Feb 23 2018 00:28:33
%S 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,
%T 28,18,29,33,35,10,45,30,50,31,34,37,41,38,40,39,55,43,36,42,49,44,57,
%U 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
%N Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 5, and no term occurs twice.
%C A permutation of the positive integers.
%e a(1) = 1 is the least positive integer, and a(1) has no other constraint to satisfy.
%e a(2) = 5 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 5 has a digit 5.
%e 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.
%e 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.
%o (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}
%Y Cf. A299402, A299403, A298974, ..., A298979: analog with digit 2, 3; ..., 9.
%Y Cf. A299957, A299969, ..., A299988 (analog with addition instead of multiplication, and different digits).
%K nonn,base
%O 1,2
%A _M. F. Hasler_, Feb 22 2018
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