A342802 Replace 2^k with (-3)^k in binary expansion of n.

0, 1, -3, -2, 9, 10, 6, 7, -27, -26, -30, -29, -18, -17, -21, -20, 81, 82, 78, 79, 90, 91, 87, 88, 54, 55, 51, 52, 63, 64, 60, 61, -243, -242, -246, -245, -234, -233, -237, -236, -270, -269, -273, -272, -261, -260, -264, -263, -162, -161, -165, -164, -153, -152, -156, -155, -189, -188, -192, -191, -180, -179, -183, -182

Offset

0,3

Comments

All terms correspond to a sum of distinct powers of -3.

Links

Wyatt Powers, Table of n, a(n) for n = 0..9999

Example

For n = 0, a(0) = 0.
for n = 1, a(1) = -3^0 = 1.
for n = 2, a(2) = -3^1 = -3.
for n = 3, a(3) = -3^1 + -3^0 = -2.
for n = 4, a(4) = -3^2 = 9.
for n = 5, a(5) = -3^2 + -3^0 = 10.

Mathematica

(* Returns first 100 numbers in the sequence; assigned to the list, a *)
a = Table[IntegerDigits[x, 2], {x, 0, 100}];
For[i = 1, i <= Length[a], i++,
  For[j = 1, j <= Length[a[[i]]], j++,
   a[[i]][[j]] = ((a[[i]][[j]])*(-3)^(Length[a[[i]]] - j))
   ]
  ];
For[i = 1, i <= Length[a], i++, a[[i]] = Total[a[[i]]]];
a

Prog

(PARI) a(n) = my(b=Vecrev(binary(n))); sum(k=1, #b, b[k]*(-3)^(k-1)); \\ Michel Marcus, Mar 22 2021
(PARI) a(n) = fromdigits(binary(n), -3) \\ Kevin Ryde, Mar 22 2021
(Python)
def a(n):
  return sum((-3)**k for k, b in enumerate(bin(n)[2:][::-1]) if b=='1')
print([a(n) for n in range(64)]) # Michael S. Branicky, Mar 23 2021

Crossrefs

Cf. A005836 (sums of distinct powers of 3), A053985, A065369.

Sequence in context: A152049 A246788 A365278 * A099887 A366348 A274827

Adjacent sequences: A342799 A342800 A342801 * A342803 A342804 A342805

Keyword

sign,look,easy,base

Author

Wyatt Powers, Mar 21 2021

Status

approved