A309477 -id:A309477 - cp's OEIS frontend

A309475 Digits of one of the two 3-adic integers sqrt(-1/2). Here the sequence with first digit 2.

2, 0, 1, 0, 0, 1, 0, 2, 1, 1, 1, 2, 0, 1, 0, 2, 1, 0, 2, 1, 2, 2, 1, 0, 2, 0, 1, 1, 1, 0, 0, 0, 1, 2, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 2, 1, 0, 1, 1, 1, 2, 1, 2, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 0, 2, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 1, 0, 2, 2, 2

Offset: 0

Seiichi Manyama, Aug 04 2019

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A271224, A309474, A309477.

T:= select(t -> padic:-ratvaluep(t, 1)=2, [padic:-rootp(x^2+1/2, 3, 100)]): op([1, 1, 3], T); # Robert Israel, Aug 05 2019

Vecrev(digits(truncate(-sqrt(-1/2+O(3^100))), 3))

p           = ...100102, p^2   = ...111111.
q = A271224 = ...022012, p * q = ...000001.
a(n) = (b(n+1) - b(n))/3^n, with b(n) = A309477(n).

A309476 One of the two successive approximations up to 3^n for the 3-adic integer sqrt(-1/2).

Original entry on oeis.org

0, 1, 7, 16, 70, 232, 475, 1933, 1933, 8494, 28177, 87226, 87226, 1150108, 2744431, 12310369, 12310369, 55357090, 313637416, 313637416, 1475898883, 1475898883, 1475898883, 32856958492, 221143316146, 221143316146, 1915720535032, 4457586363361, 12083183848348, 34959976303309

Offset: 0

Seiichi Manyama, Aug 04 2019

nonn

			a(1) = (   1)_3 = 1,
a(2) = (  21)_3 = 7,
a(3) = ( 121)_3 = 16,
a(4) = (2121)_3 = 70.

Robert Israel, Table of n, a(n) for n = 0..2093

Cf. A268924, A309474, A309477.

N:= 30: # for a(0) to a(N)
with(padic):
A:= rootp(x^2+1/2,3,N):
if ratvaluep(A[1],1) = 1 then A:= A[1] else A:= A[2] fi:
seq(ratvaluep(A,i),i=0..N); # Robert Israel, May 11 2020

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

cp's OEIS Frontend

A309475 Digits of one of the two 3-adic integers sqrt(-1/2). Here the sequence with first digit 2.

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