A347412 Sqrt(3)+1-adic expansion of 4, in binary alphabet

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

Offset

0

Comments

Similarly to A347411, start with the number 4, and repeatedly "carry" into higher terms of the sequence by scaling and shifting the sequence (-2, -2, 1). For negative odd numbers, carry past 0 so that the result of the carry is 1.

Links

Table of n, a(n) for n=0..255.

Example

First few iterates of carry, starting from expansion "4":
4
0, -4, 2
0, 0, 6, -2
0, 0, 0, -8, 3
0, 0, 0,  0, 11, 4
0, 0, 0,  0,  1, -14, 5
0, 0, 0,  0,  1,   0, 19, -7
0, 0, 0,  0,  1,   0,  1, -25, 9
0, 0, 0,  0,  1,   0,  1,   1, 35, -13

Prog

(Haskell)
a347412_iterates = iterate (doubleBorrow []) (4:repeat 0) where
  doubleBorrow zs (x:y:z:xs)
    | odd x && x <= -2 = let (q, r) = quotRem x 2 in foldl (flip (:)) (r + 2 : y-x+r+2 : z+q-1 : xs) zs
    | abs x >= 2       = let (q, r) = quotRem x 2 in foldl (flip (:)) (r : y-x+r : z+q : xs) zs
    | otherwise  = doubleBorrow (x:zs) (y:z:xs)
a347412 n = (a347412_iterates !! (n+1)) !! n

Crossrefs

Cf. A347411

Sequence in context: A347411 A059437 A152592 * A275926 A131533 A131532

Adjacent sequences: A347409 A347410 A347411 * A347413 A347414 A347415

Keyword

nonn,base

Author

Ben Conner, Aug 30 2021

Extensions

Extra-long data section is OK for now. - N. J. A. Sloane, Oct 25 2021

Status

approved