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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A permutation of the positive integers. LINKS 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: A167583 A329029 A248983 * A070375 A162813 A166465 Adjacent sequences:  A298972 A298973 A298974 * A298976 A298977 A298978 KEYWORD nonn,base AUTHOR M. F. Hasler, Feb 22 2018 STATUS approved

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Last modified December 9 19:51 EST 2019. Contains 329879 sequences. (Running on oeis4.)