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A048899
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Successive approximations up to 5^n for 5-adic integer sqrt(-1).
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4
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0, 3, 18, 68, 443, 1068, 1068, 32318, 110443, 1672943, 3626068, 23157318, 120813568, 1097376068, 1097376068, 19407922943, 49925501068, 355101282318, 355101282318, 15613890344818, 15613890344818, 110981321985443
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| This is the root congruent to 3 (mod 5).
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REFERENCES
| K. Mahler, Introduction to p-Adic Numbers and Their Functions, Cambridge, 1973, p. 35.
J. H. Conway, The Sensual Quadratic Form, p. 118.
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FORMULA
| a(n) = 5^n - A048898(n) = A066601(5^n).
0 <= a(n) < 5^n. 5^n divides a(n)^2 + 1.
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EXAMPLE
| a(2) = 7 because the two roots of x^2 + 1 == 0 (mod 5^2) are 7 and 18 and 7 == 3 (mod 5).
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PROG
| (PARI) {a(n) = if( n<2, 3, a(n - 1)^5) % 5^n}
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CROSSREFS
| Cf. A048898, A066601.
Sequence in context: A110689 A027333 A026576 * A107583 A157535 A098522
Adjacent sequences: A048896 A048897 A048898 * A048900 A048901 A048902
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KEYWORD
| nonn,easy
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AUTHOR
| Michael Somos, Mar 03 2008
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