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A253389 Repeating digit pattern in penultimate digit of successive powers of each integer starting with 2 (skipping powers that do not have at least two digits) 0
13625124998637487500, 28428684442602686000, 1652983470, 2, 31975, 4400, 8264462800, 0, 1234567890 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

This is looking one step past the well-known rules for the last digit of successive powers:  Powers of integers ending in digit 2 always repeat 2486 in the last digit pattern, powers of integers ending in digit 3 always repeat 3971, of integers ending in 4 repeat 46, of integers ending in 1, 5, and 6 repeat themselves, of integers ending in 7 repeat 7931, of integers ending in 8 repeat 8426, and of integers ending in 9 repeat 91.

Is there a pattern in the repeating patterns in the penultimate digits?  Possibly 99 patterns, for x = 01 to 99?

LINKS

Table of n, a(n) for n=2..10.

EXAMPLE

Powers of 2:

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096...

Second-to-the-last digits, skipping the one-digit powers:  1,3,6,2,5,1,2,4,9,9,8,6...

Find repeating pattern and concatenate digits:  13625124998637487500

10 does not repeat its penultimate digit (1), so a(10)=0.

CROSSREFS

Cf. A160590 (penultimate digit of 2^n).

Sequence in context: A155960 A266961 A238359 * A257307 A115540 A104263

Adjacent sequences:  A253386 A253387 A253388 * A253390 A253391 A253392

KEYWORD

nonn,base

AUTHOR

Erik Maher, Dec 31 2014

STATUS

approved

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)