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A322561 Digits of one of the two 17-adic integers sqrt(2) that is related to A322559. 6
6, 14, 14, 8, 5, 4, 14, 14, 7, 2, 15, 15, 11, 5, 6, 7, 2, 14, 6, 14, 15, 16, 3, 8, 14, 5, 12, 16, 0, 4, 7, 0, 8, 10, 2, 16, 16, 15, 9, 7, 12, 9, 14, 14, 5, 12, 3, 4, 7, 9, 9, 2, 2, 14, 5, 9, 12, 6, 2, 10, 5, 0, 10, 10, 11, 11, 2, 3, 14, 10, 11, 2, 6, 12, 0, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This square root of 2 in the 17-adic field ends with digit 6. The other, A322562, ends with digit 11 (B when written as a 17-adic number).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Wikipedia, p-adic number

FORMULA

a(n) = (A322559(n+1) - A322559(n))/17^n.

For n > 0, a(n) = 16 - A322562(n).

Equals A309989*A322566 = A309990*A322565.

EXAMPLE

The solution to x^2 == 2 (mod 17^4) such that x == 6 (mod 17) is x == 43594 (mod 17^4), and 43594 is written as 8EE6 in heptadecimal, so the first four terms are 6, 14, 14 and 8.

PROG

(PARI) a(n) = truncate(sqrt(2+O(17^(n+1))))\17^n

CROSSREFS

Cf. A322559, A322560.

Digits of 17-adic square roots:

A309989, A309990 (sqrt(-1));

this sequence, A322562 (sqrt(2));

A322565, A322566 (sqrt(-2)).

Sequence in context: A265029 A329065 A184998 * A079010 A324814 A015822

Adjacent sequences:  A322558 A322559 A322560 * A322562 A322563 A322564

KEYWORD

nonn,base

AUTHOR

Jianing Song, Aug 29 2019

STATUS

approved

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Last modified May 25 16:40 EDT 2020. Contains 334595 sequences. (Running on oeis4.)