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A341652 Numbers j > 1 at which the absolute difference between log(j)*log(A341651(j)) and the nearest integer reaches a record low. 4
2, 3, 4, 6, 11, 12, 53, 60, 146, 315, 328, 391, 438, 509, 659, 883, 1043, 1398, 12381, 41956, 50372, 61220, 81580, 189608, 205666, 224305, 4625460, 4969792, 8505660, 12231434, 20044438, 27091898, 807041817, 2388370134, 4024950319, 5642521468, 5713420381, 9015369803 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let t(j,k) = log(j)*log(k) and let d(j,k) be the absolute difference of t(j,k) and the nearest integer, i.e., d(j,k) = |t(j,k) - round(t(j,k))|. This sequence lists the numbers j at which a record low value of d(j,k) (i.e., lower than for any other pair (j',k') satisfying 2 <= k' <= j' <= j) occurs. Corresponding values of k are in A341653.

Viewed on a log-log scatterplot (see links), the records at a(6)=12 (see A341651), a(18)=1398 (see A341577), a(26)=224305, and a(32)=27091898 are among the most noteworthy; at each of these, the value of d(j,k) is smaller than that at the previous record by at least an order of magnitude.

LINKS

Table of n, a(n) for n=1..38.

Jon E. Schoenfield, Magma program

Jon E. Schoenfield, scatterplot

EXAMPLE

   n        a(n)  A341653(n)     d(a(n), A341653(n))

  --  ----------  ----------  --------------------------

   1           2           2  0.480453013918201424667...

   2           3           3  0.206948960812581977843...

   3           4           2  0.039093972163597150665...

   4           6           3  0.031551028768609035727...

   5          11           8  0.013716957145365614933...

   6          12           5  0.000697028971586630527...

   7          53          34  0.000680675152963635202...

   8          60          39  0.000116295803634252268...

   9         146         101  0.000054832287899364403...

  10         315         310  0.000048839123899624765...

  11         328          53  0.000044915535035844255...

  12         391         213  0.000014919239839943413...

  13         438         372  0.000008128971060973828...

  14         509         234  0.000005265057291740358...

  15         659         299  0.000003258910498615529...

  16         883         314  0.000002329487103416809...

  17        1043         865  0.000000682825287407936...

  18        1398         658  0.000000002813997334219...

  19       12381       11361  0.000000000872119900887...

  20       41956       14509  0.000000000814175918916...

  21       50372        7777  0.000000000745870254123...

  22       61220       16443  0.000000000305254102745...

  23       81580       48414  0.000000000119066473361...

  24      189608        5207  0.000000000098904866606...

  25      205666      101240  0.000000000041317761770...

  26      224305      193798  0.000000000000279730065...

  27     4625460     3442529  0.000000000000166375004...

  28     4969792     1213224  0.000000000000027648926...

  29     8505660     4961227  0.000000000000009234703...

  30    12231434     9975776  0.000000000000003807238...

  31    20044438    13462483  0.000000000000002464138...

  32    27091898     6698814  0.000000000000000000993...

  33   807041817   231466141  0.000000000000000000445...

  34  2388370134  2050322982  0.000000000000000000225...

  35  4024950319  1774903846  0.000000000000000000098...

  36  5642521468  4287949990  0.000000000000000000086...

  37  5713420381   815914629  0.000000000000000000045...

  38  9015369803  7431998815  0.000000000000000000029...

CROSSREFS

Cf. A341577, A341651, A341653.

Sequence in context: A245569 A018297 A050886 * A079310 A116853 A342334

Adjacent sequences:  A341649 A341650 A341651 * A341653 A341654 A341655

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Feb 17 2021

EXTENSIONS

Offset corrected by Chai Wah Wu, Mar 03 2021

STATUS

approved

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Last modified May 8 02:26 EDT 2021. Contains 343652 sequences. (Running on oeis4.)