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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 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.)