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A321106
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Digits of one of the three 13-adic integers 5^(1/3) that is related to A320914.
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13
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7, 0, 6, 9, 2, 12, 11, 12, 10, 3, 4, 12, 8, 12, 5, 11, 7, 8, 4, 6, 4, 3, 4, 12, 11, 9, 12, 1, 11, 5, 7, 10, 9, 5, 10, 2, 6, 11, 12, 6, 11, 6, 12, 8, 6, 11, 12, 7, 3, 2, 9, 5, 1, 12, 0, 5, 10, 3, 0, 2, 8, 3, 11, 10, 10, 2, 3, 11, 7, 1, 5, 4, 11, 10, 9, 9, 6, 3, 6, 0, 7
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OFFSET
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0,1
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COMMENTS
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For k not divisible by 5, k is a cube in 13-adic field if and only if k == 1, 5, 8, 12 (mod 13). If k is a cube in 13-adic field, then k has exactly three cubic roots.
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LINKS
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FORMULA
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EXAMPLE
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The unique number k in [1, 13^3] and congruent to 7 modulo 13 such that k^3 - 5 is divisible by 13^3 is k = 1021 = (607)_13, so the first three terms are 7, 0 and 6.
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PROG
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(PARI) a(n) = lift(sqrtn(5+O(13^(n+1)), 3) * (-1+sqrt(-3+O(13^(n+1))))/2)\13^n
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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