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 A290806 One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-5). These are the numbers congruent to 3 mod 7 (except for the initial 0). 10
 0, 3, 17, 311, 997, 3398, 20205, 608450, 2255536, 25314740, 25314740, 307789989, 8217096961, 77423532966, 368090564187, 4437429001281, 4437429001281, 4437429001281, 4437429001281, 3261264624822179, 3261264624822179, 3261264624822179, 1120352992791390193 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS x   = ...112623, x^2 = ...666662 = -5. LINKS Robert Israel, Table of n, a(n) for n = 0..1182 Wikipedia, Hensel's Lemma. FORMULA a(0) = 0 and a(1) = 3, a(n) = a(n-1) + (a(n-1)^2 + 5) mod 7^n for n > 1. EXAMPLE a(1) =    3_7 = 3, a(2) =   23_7 = 17, a(3) =  623_7 = 311, a(4) = 2623_7 = 997. MAPLE with(padic): R:= [rootp(x^2+5, 7, 100)]: R1:= op(select(t -> ratvaluep(evalp(t, 7, 1))=3, R)): seq(ratvaluep(evalp(R1, 7, n)), n=0..100); # Robert Israel, Aug 13 2017 PROG (PARI) a(n) = if (n, truncate(sqrt(-5+O(7^(n)))), 0) CROSSREFS Cf. A290798, A290809. Sequence in context: A155201 A062622 A271609 * A009592 A051294 A192556 Adjacent sequences:  A290803 A290804 A290805 * A290807 A290808 A290809 KEYWORD nonn AUTHOR Seiichi Manyama, Aug 11 2017 STATUS approved

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Last modified October 22 19:53 EDT 2019. Contains 328319 sequences. (Running on oeis4.)