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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

Table of n, a(n) for n=2..72.

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.)