A359698 Least k > 0 such that the first n digits of 2^k and 3^k are identical.

1, 17, 193, 619, 2016, 91958, 91958, 8186278, 45392361, 977982331, 26450915298, 91600221212, 196425900073, 14810317269038, 44430951807114, 626642721222487, 626642721222487, 102882886570917135, 874191214492184404, 3830977578643912683, 86801197487071715103

Offset

0,2

Links

Zhao Hui Du, Table of n, a(n) for n = 0..1000

Example

   n    k = a(n)   1st n digits
  --  -----------  -------------
   0            1
   1           17  1...
   2          193  12...
   3          619  217...
   4         2016  7524...
   5        91958  13071...
   6        91958  130719...
   7      8186278  1701547...
   8     45392361  17179395...
   9    977982331  725070476...
  10  26450915298  2919267309...
a(3) = 619 because 2^619 = 2.175...*10^186 and 3^619 = 2.177...*10^295 both begin with the same three digits (in base ten), and this is not true of any smaller positive integer than 619.
a(0) = 1 because 2^1 and 3^1 share zero leading digits.

Crossrefs

Cf. A000079, A000244, A088995.

Sequence in context: A300172 A160658 A140537 * A021434 A019316 A262111

Adjacent sequences: A359695 A359696 A359697 * A359699 A359700 A359701

Keyword

base,nonn

Author

Keith F. Lynch, May 20 2023

Extensions

a(11)-a(20) from Jon E. Schoenfield, May 21 2023

Status

approved