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 A299402 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 2, and no term occurs twice. 14
 1, 2, 6, 4, 3, 7, 16, 8, 9, 14, 13, 17, 12, 10, 20, 11, 19, 15, 18, 24, 5, 25, 21, 22, 26, 27, 23, 34, 28, 29, 32, 31, 33, 37, 35, 36, 42, 30, 40, 38, 39, 48, 43, 44, 46, 45, 47, 41, 49, 50, 51, 52, 53, 54, 55, 59, 58, 56, 57, 60, 62, 61, 66, 64, 63, 67, 69, 68, 65, 80, 74, 71, 72, 73, 77, 76, 70, 75, 79, 78, 84, 83, 81, 82, 86, 87, 95, 96, 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, it has no other requirement to satisfy. a(2) = 2 is the least positive integer > a(1) = 1, and a(2)*a(1) = 2 has a digit 2. a(3) = 6 is the least positive integer > a(2) = 2 such that a(3)*a(2) (= 12) has a digit 2: The smaller choices 3, 4 or 5 do not satisfy this. a(4) = 4 is the least positive integer > a(2) = 2 such that a(4)*a(3) (= 24) has a digit 2: The smaller choice 3 yields 3*6 = 18 and does not satisfy this. Now, the least available positive integer a(5) = 3 is such that 3*4 = 12, which has again a digit 2. And so on. PROG (PARI) a(n, f=1, d=2, 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. A299403, A298974, ..., A298979 (analog with digit 3, ..., 9). Cf. A299957, A299969, ..., A299988 (analog with addition instead of multiplication, and different digits). Sequence in context: A283614 A003571 A068457 * A286451 A102510 A206225 Adjacent sequences:  A299399 A299400 A299401 * A299403 A299404 A299405 KEYWORD nonn,base AUTHOR M. F. Hasler, Feb 22 2018 STATUS approved

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)