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 A051277 Coefficients in 7-adic expansion of sqrt(2). 12
 3, 1, 2, 6, 1, 2, 1, 2, 4, 6, 6, 2, 1, 1, 0, 2, 1, 1, 4, 6, 1, 3, 2, 6, 6, 3, 5, 5, 6, 3, 4, 5, 0, 1, 6, 3, 0, 4, 6, 2, 4, 4, 6, 4, 2, 4, 4, 2, 6, 1, 3, 4, 1, 3, 1, 4, 2, 6, 6, 0, 3, 5, 5, 1, 1, 2, 0, 6, 6, 1, 1, 2, 4, 4, 4, 2, 3, 6, 6, 3, 6, 1, 4, 4, 2, 2, 1, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES Alf van der Poorten, Notes on Fermat's Last Theorem, Wiley, 1996, p. 76. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 Peter Bala, Using Chebyshev polynomials to find the p-adic square roots of 2 and 3, Dec 2022. FORMULA Equals the 7-adic limit as n -> oo of 2*T(7^n,3/2) = the 7-adic limit as n -> oo of ((3 + sqrt(5))/2)^(7^n) + ((3 - sqrt(5))/2)^(7^n), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. - Peter Bala, Nov 20 2022 EXAMPLE 3 + 7 + 2*7^2 + 6*7^3 + 7^4 + 2*7^5 + 7^6 + ... MAPLE t := proc(n) option remember; if n = 1 then 3 else irem(t(n-1)^7 - 7*t(n-1)^5 + 14*t(n-1)^3 - 7*t(n-1), 7^n) end if; end: convert(t(100), base, 7); # Peter Bala, Nov 20 2022 PROG (PARI) Vecrev(digits(lift(sqrt(2+O(7^99))), 7)) \\ Joerg Arndt, Aug 05 2017 CROSSREFS Cf. A034945, A290558. Sequence in context: A049919 A246432 A112571 * A300908 A080818 A334354 Adjacent sequences: A051274 A051275 A051276 * A051278 A051279 A051280 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane EXTENSIONS Missing terms=0 inserted by Seiichi Manyama, Aug 04 2017 STATUS approved

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Last modified September 27 12:14 EDT 2023. Contains 365691 sequences. (Running on oeis4.)