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A290809
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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 4 mod 7 (except for the initial 0).
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10
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0, 4, 32, 32, 1404, 13409, 97444, 215093, 3509265, 15038867, 257160509, 1669536754, 5624190240, 19465477441, 310132508662, 310132508662, 28795501568320, 228193084985926, 1623976168909168, 8137630560550964, 76531001672789822, 555284599458461828
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OFFSET
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0,2
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COMMENTS
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x = ...554044,
x^2 = ...666662 = -5.
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LINKS
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FORMULA
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a(0) = 0 and a(1) = 4, a(n) = a(n-1) + 6 * (a(n-1)^2 + 5) mod 7^n for n > 1.
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EXAMPLE
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a(1) = 4_7 = 4,
a(2) = 44_7 = 32,
a(3) = 44_7 = 32,
a(4) = 4044_7 = 1404.
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PROG
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(PARI) a(n) = if (n, 7^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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