A135358 Numbers n such that 7^n and 7^(n+1) have the same number of decimal digits.

6, 12, 19, 25, 32, 38, 45, 51, 58, 64, 71, 77, 83, 90, 96, 103, 109, 116, 122, 129, 135, 142, 148, 154, 161, 167, 174, 180, 187, 193, 200, 206, 213, 219, 225, 232, 238, 245, 251, 258, 264, 271, 277, 284, 290, 296, 303, 309, 316, 322, 329, 335, 342, 348, 355

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

Sequence in context: A344177 A100357 A190265 * A187391 A081846 A078816

Adjacent sequences: A135355 A135356 A135357 * A135359 A135360 A135361

Keyword

base,nonn

Author

Zak Seidov, Dec 08 2007

Status

approved