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 A299996 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 6, and no term occurs twice. 10
 1, 6, 10, 16, 4, 9, 7, 8, 2, 3, 12, 5, 13, 20, 18, 17, 28, 22, 21, 26, 11, 15, 24, 14, 19, 32, 23, 27, 25, 64, 29, 34, 39, 35, 36, 31, 44, 37, 38, 42, 30, 52, 33, 49, 40, 41, 43, 48, 45, 57, 46, 47, 56, 51, 60, 61, 65, 71, 53, 50, 72, 55, 63, 58, 62, 59, 54, 66, 70, 67, 68, 69, 74, 76, 79, 73, 77, 78, 80, 75, 81, 82, 83, 84, 89, 85, 90, 94, 92 (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) = 6 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 6 has a digit 6. a(3) = 10 is the least positive integer not in {1, 6} such that a(3)*a(2) (= 60) has a digit 6: All smaller choices (2, 3, 4 or 5) do not satisfy this. a(4) = 16 is the least positive integer not in {1, 6, 10} such that a(4)*a(3) (= 160) has a digit 6: All smaller choices 2,...,15 do not satisfy this. PROG (PARI) A299996(n, f=1, d=6, 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, A299997: analog with digit 2, 3, ..., 9, 7. Cf. A299957, A299969, ..., A299988 (analog with addition instead of multiplication, and different digits). Sequence in context: A319035 A117309 A228300 * A315289 A108936 A315290 Adjacent sequences:  A299993 A299994 A299995 * A299997 A299998 A299999 KEYWORD nonn,base AUTHOR M. F. Hasler, Feb 22 2018 STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)