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 A341651 a(n) is the integer k in the interval [2,n] at which log(n)*log(k) is closest to an integer. 3
 2, 3, 2, 2, 3, 5, 7, 4, 9, 8, 5, 7, 14, 3, 6, 17, 2, 15, 20, 10, 7, 13, 17, 12, 16, 21, 11, 8, 19, 25, 32, 31, 30, 22, 7, 4, 3, 3, 34, 33, 19, 11, 31, 18, 23, 38, 48, 47, 10, 35, 27, 34, 43, 20, 12, 32, 15, 31, 39, 7, 38, 23, 29, 11, 58, 57, 35, 17, 27, 54, 42 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS a(1398) = 658; log(1398)*log(658) = 46.999999997186..., a result remarkably close to an integer (see A341577). Values of j and k (2 <= k <= j) at which the absolute difference between log(j)*log(k) and the nearest integer reaches a record low as j runs through the positive integers are in A341652 and A3416523, respectively. LINKS EXAMPLE For n=2, the only integer k in the interval [2,n] is 2, so a(2) = 2. For n=3, log(3)*log(2) = 0.76150..., which differs from the nearest integer (1) by 0.23849..., but log(3)*log(3) = 1.20694..., which differs from the nearest integer (again, 1) by only 0.20694..., which is less than 0.23849..., so a(3) = 3. For n=12, we have    k  P=log(12)*log(k)   |P - round(P)|   --  ----------------  ----------------    2  1.72240603825...  0.27759396174...    3  2.72994898165...  0.27005101834...    4  3.44481207651...  0.44481207651...    5  3.99930297102...  0.00069702897... (minimum)    6  4.45235501990...  0.45235501990...    7  4.83540506927...  0.16459493072...    8  5.16721811476...  0.16721811476...    9  5.45989796330...  0.45989796330...   10  5.72170900928...  0.27829099071...   11  5.95854590887...  0.04145409112...   12  6.17476105816...  0.17476105816... so a(12) = 5. CROSSREFS Cf. A341577, A341652, A341653. Sequence in context: A053812 A177865 A307835 * A017828 A140087 A174329 Adjacent sequences:  A341648 A341649 A341650 * A341652 A341653 A341654 KEYWORD nonn AUTHOR Jon E. Schoenfield, Feb 17 2021 STATUS approved

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Last modified May 13 07:08 EDT 2021. Contains 343836 sequences. (Running on oeis4.)