

A325893


The successive approximations up to 2^n for 2adic integer 5^(1/5).


4



0, 1, 1, 5, 5, 21, 21, 21, 149, 149, 149, 1173, 1173, 1173, 9365, 9365, 42133, 107669, 238741, 500885, 1025173, 1025173, 1025173, 1025173, 1025173, 1025173, 34579605, 34579605, 34579605, 34579605, 571450517, 1645192341, 1645192341, 1645192341, 10235126933, 10235126933
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OFFSET

0,4


COMMENTS

a(n) is the unique solution to x^5 == 5 (mod 2^n) in the range [0, 2^n  1].


LINKS



FORMULA

For n > 0, a(n) = a(n1) if a(n1)^5  5 is divisible by 2^n, otherwise a(n1) + 2^(n1).


EXAMPLE

For n = 2, the unique solution to x^5 == 5 (mod 4) in the range [0, 3] is x = 1, so a(2) = 1.
a(2)^5  5 = 4 which is not divisible by 8, so a(3) = a(2) + 4 = 5;
a(3)^5  5 = 3120 which is divisible by 16, so a(4) = a(3) = 5;
a(4)^5  5 = 3120 which is not divisible by 32, so a(5) = a(4) + 16 = 21;
a(5)^5  5 = 4084096 which is divisible by 64, so a(6) = a(5) = 21.


PROG

(PARI) a(n) = lift(sqrtn(5+O(2^n), 5))


CROSSREFS

For the digits of 5^(1/5), see A325897.
Approximations of padic fifthpower roots:
this sequence (2adic, 5^(1/5));


KEYWORD

nonn


AUTHOR



STATUS

approved



