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A290806
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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).
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10
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0, 3, 17, 311, 997, 3398, 20205, 608450, 2255536, 25314740, 25314740, 307789989, 8217096961, 77423532966, 368090564187, 4437429001281, 4437429001281, 4437429001281, 4437429001281, 3261264624822179, 3261264624822179, 3261264624822179, 1120352992791390193
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OFFSET
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0,2
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COMMENTS
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x = ...112623,
x^2 = ...666662 = -5.
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LINKS
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FORMULA
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a(0) = 0 and a(1) = 3, a(n) = a(n-1) + (a(n-1)^2 + 5) mod 7^n for n > 1.
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EXAMPLE
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a(1) = 3_7 = 3,
a(2) = 23_7 = 17,
a(3) = 623_7 = 311,
a(4) = 2623_7 = 997.
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MAPLE
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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
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PROG
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(PARI) a(n) = if (n, truncate(sqrt(-5+O(7^(n)))), 0)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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