A341540 - OEIS

A341540

Expansion of the 2-adic integer sqrt(17) that ends in 11.

1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1

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OFFSET

COMMENTS

Over the 2-adic integers there are 2 solutions to x^2 = 17, one ends in 01 and the other ends in 11. This sequence gives the latter one. See A341539 for detailed information.

LINKS

Jianing Song, Table of n, a(n) for n = 0..1000

FORMULA

a(0) = 1, a(1) = 0; for n >= 2, a(n) = 0 if A341539(n)^2 - 17 is divisible by 2^(n+2), otherwise 1.

a(n) = 1 - A322217(n) for n >= 1.

For n >= 2, a(n) = (A341539(n+1) - A341539(n))/2^n.

EXAMPLE

If x = ...00000110011001100001011001101100100010111, then x^2 = 10001_2 = 17.

PROG

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

CROSSREFS

Cf. A322217, A341539 (successive approximations of the associated 2-adic square root of 17), A318962, A318963 (expansion of sqrt(-7)).