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%I #22 Oct 25 2022 17:12:54
%S 6,12,19,25,32,38,45,51,58,64,71,77,83,90,96,103,109,116,122,129,135,
%T 142,148,154,161,167,174,180,187,193,200,206,213,219,225,232,238,245,
%U 251,258,264,271,277,284,290,296,303,309,316,322,329,335,342,348,355
%N Numbers n such that 7^n and 7^(n+1) have the same number of decimal digits.
%C 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
%H G. C. Greubel, <a href="/A135358/b135358.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1)=6 because {7^6, 7^7} = {117649, 823543} (6 digits),
%e a(2)=12 because {7^12,7^13}={13841287201,96889010407} (11 digits).
%e Sequence of first differences are only quasi-periodic:
%e 6,7,6,7,6,7,6,7,6,7,6,6,7,
%e 6,7,6,7,6,7,6,7,6,6,7,
%e 6,7,6,7,6,7,6,7,6,6,7,
%e 6,7,6,7,6,7,6,7,6,6,7,
%e 6,7,6,7,6,7,6,7,6,6,7,
%e 6,7,6,7,6,7,6,7,6,6,7,
%e 6,7,6,7,6,7,6,7,6,7,6,6,7.
%t Select[Range[100], IntegerLength[7^(#)] == IntegerLength[7^(# + 1)] &] (* _G. C. Greubel_, Oct 11 2016 *)
%t SequencePosition[IntegerLength/@(7^Range[400]),{x_,x_}][[All,1]]((* Requires Mathematica version 10 or later *) * _Harvey P. Dale_, Feb 14 2020 *)
%o (PARI) isok(n) = #digits(7^n) == #digits(7^(n+1)); \\ _Michel Marcus_, Oct 13 2013
%K base,nonn
%O 1,1
%A _Zak Seidov_, Dec 08 2007
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