OFFSET
1,1
COMMENTS
The linear recurrence of order 12 with signature (1,0,0,0,0,0,0,0,0,0,1,-1) is incorrect, it yields 509 instead of a(79) = 510. - Georg Fischer, Oct 25 2022
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
EXAMPLE
a(1)=6 because {7^6, 7^7} = {117649, 823543} (6 digits),
a(2)=12 because {7^12,7^13}={13841287201,96889010407} (11 digits).
Sequence of first differences are only quasi-periodic:
6,7,6,7,6,7,6,7,6,7,6,6,7,
6,7,6,7,6,7,6,7,6,6,7,
6,7,6,7,6,7,6,7,6,6,7,
6,7,6,7,6,7,6,7,6,6,7,
6,7,6,7,6,7,6,7,6,6,7,
6,7,6,7,6,7,6,7,6,6,7,
6,7,6,7,6,7,6,7,6,7,6,6,7.
MATHEMATICA
Select[Range[100], IntegerLength[7^(#)] == IntegerLength[7^(# + 1)] &] (* G. C. Greubel, Oct 11 2016 *)
SequencePosition[IntegerLength/@(7^Range[400]), {x_, x_}][[All, 1]]((* Requires Mathematica version 10 or later *) * Harvey P. Dale, Feb 14 2020 *)
PROG
(PARI) isok(n) = #digits(7^n) == #digits(7^(n+1)); \\ Michel Marcus, Oct 13 2013
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Zak Seidov, Dec 08 2007
STATUS
approved