login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A341600 One of the two successive approximations up to 2^n for 2-adic integer sqrt(-3/5). This is the 1 (mod 4) case. 3
1, 5, 5, 5, 5, 69, 197, 453, 453, 1477, 3525, 3525, 3525, 3525, 3525, 3525, 134597, 396741, 396741, 1445317, 1445317, 1445317, 9833925, 26611141, 60165573, 127274437, 261492165, 529927621, 1066798533, 2140540357, 2140540357, 2140540357, 10730474949, 27910344133 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

a(n) is the unique number k in [1, 2^n] and congruent to 1 mod 4 such that 5*k^2 + 3 is divisible by 2^(n+1).

LINKS

Jianing Song, Table of n, a(n) for n = 2..1000

FORMULA

a(2) = 1; for n >= 3, a(n) = a(n-1) if 5*a(n-1)^2 + 3 is divisible by 2^(n+1), otherwise a(n-1) + 2^(n-1).

a(n) = 2^n - A341601(n).

a(n) = Sum_{i=0..n-1} A341602(i)*2^i.

EXAMPLE

The unique number k in [1, 4] and congruent to 1 modulo 4 such that 5*k^2 + 3 is divisible by 8 is 1, so a(2) = 1.

5*a(2)^2 + 3 = 8 which is not divisible by 16, so a(3) = a(2) + 2^2 = 5.

5*a(3)^2 + 3 = 128 which is divisible by 32, 64 and 128, so a(6) = a(5) = a(4) = a(3) = 5.

...

PROG

(PARI) a(n) = truncate(-sqrt(-3/5+O(2^(n+1))))

CROSSREFS

Cf. A341601 (the 3 (mod 4) case), A341602 (digits of the associated 2-adic square root of -3/5), A318960, A318961 (successive approximations of sqrt(-7)), A341538, A341539 (successive approximations of sqrt(17)).

Sequence in context: A082476 A024729 A046271 * A283076 A046263 A092279

Adjacent sequences:  A341597 A341598 A341599 * A341601 A341602 A341603

KEYWORD

nonn

AUTHOR

Jianing Song, Feb 16 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 1 16:18 EDT 2022. Contains 354973 sequences. (Running on oeis4.)