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 A055620 Digits of an idempotent 6-adic number. 7
 4, 4, 3, 5, 0, 2, 4, 3, 3, 3, 0, 4, 0, 0, 4, 1, 4, 2, 4, 3, 0, 0, 0, 5, 0, 3, 0, 0, 0, 2, 4, 1, 2, 2, 5, 1, 3, 3, 1, 5, 4, 2, 2, 4, 1, 5, 3, 5, 4, 3, 0, 3, 1, 5, 3, 2, 2, 5, 2, 1, 0, 0, 3, 0, 0, 1, 2, 3, 2, 4, 0, 1, 0, 1, 5, 4, 4, 5, 1, 3, 5, 4, 2, 5, 4, 0, 5, 1, 2, 0, 5, 4, 5, 3, 1, 5, 2, 1, 3, 3, 2, 3, 3, 5, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS ( a(0) + a(1)*6 + a(2)*6^2 + ... )^k = a(0) + a(1)*6 + a(2)*6^2 + ... for each k. Apart from 0 and 1 in base 6 there are only 2 numbers with this property. For the other see A054869. REFERENCES V. deGuerre and R. A. Fairbairn, Automorphic numbers, J. Rec. Math., 1 (No. 3, 1968), 173-179. LINKS Kenny Lau, Table of n, a(n) for n = 0..9999 V. deGuerre and R. A. Fairbairn, Automorphic numbers, J. Rec. Math., 1 (No. 3, 1968), 173-179. FORMULA If A is the 6-adic number, A == 4^(3^n) mod 6^n. - Robert Dawson, Oct 28 2022 EXAMPLE (a(0) + a(1)*6 + a(2)*6^2 + a(3)*6^3)^2 == (a(0) + a(1)*6 + a(2)*6^2 + a(3)*6^3) mod 6^4 because 1478656 == 1216 (mod 1296). PROG (Python) n=10000; res=pow((3**n+1)//2, n, 3**n)*2**n for i in range(n):print(i, res%6); res//=6 # Kenny Lau, Jun 09 2018 (PARI) first(p)=Vecrev(digits(lift(Mod(4, 6^p)^3^p), 6)) \\ Charles R Greathouse IV, Nov 01 2022 CROSSREFS The six examples given by deGuerre and Fairbairn are A055620, A054869, A018247, A018248, A259468, A259469. Sequence in context: A106147 A202393 A073321 * A072420 A258075 A286296 Adjacent sequences: A055617 A055618 A055619 * A055621 A055622 A055623 KEYWORD nonn,base AUTHOR Paolo Dominici (pl.dm(AT)libero.it), Jun 04 2000 STATUS approved

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Last modified September 19 01:02 EDT 2024. Contains 376002 sequences. (Running on oeis4.)