A037095 "Sloping binary representation" of powers of 3 (A000244), slope = -1.

1, 1, 3, 1, 3, 9, 11, 17, 19, 25, 123, 65, 195, 169, 171, 753, 435, 249, 2267, 4065, 8163, 841, 843, 31313, 29651, 39769, 38331, 30081, 160643, 49769, 53867, 563377, 700659, 1611961, 760731, 1207073, 5668771, 5566345, 11844619, 8699025, 10386067, 55868313

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Formula

a(n) = A339601(A000244(n)). - Antti Karttunen, Dec 09 2020

Example

When powers of 3 are written in binary (see A004656), under each other as:
  000000000001 (1)
  000000000011 (3)
  000000001001 (9)
  000000011011 (27)
  000001010001 (81)
  000011110011 (243)
  001011011001 (729)
  100010001011 (2187)
and one collects their bits from the column-0 to NW-direction (from the least to the most significant end), one gets 1 (1), 01 (1), 011 (3), 0001 (1), 00011 (3), 001001 (9), etc. (See A105033 for similar transformation done on nonnegative integers, A001477).

Maple

A037095:= n-> add(bit_n(3^(n-i), i)*(2^i), i=0..n):
bit_n := (x, n) -> `mod`(floor(x/(2^n)), 2):
seq(A037095(n), n=0..41);
# second Maple program:
b:= proc(n) option remember; `if`(n=0, 1, (p->
       expand((p-(p mod 2))*x/2)+3^n)(b(n-1)))
    end:
a:= n-> subs(x=2, b(n) mod 2):
seq(a(n), n=0..42);  # Alois P. Heinz, Dec 10 2020

Prog

(PARI)
A339601(n) = { my(m=1, s=0); while(n>=m, s += bitand(m, n); m <<= 1; n \= 3); (s); };
A037095(n) = A339601(3^n); \\ Antti Karttunen, Dec 09 2020
(PARI)
BINSLOPE(f) = n -> sum(i=0, n, bitand(2^(n-i), f(i))); \\ General transformation for these kinds of sequences.
A037095 = BINSLOPE(n -> 3^n); \\ And its application to A000244. - Antti Karttunen, Dec 09 2020

Crossrefs

Cf. A105033, A000244, A037093, A037094, A037096, A037097, A339601.

Sequence in context: A265307 A133579 A088442 * A160654 A146436 A058842

Adjacent sequences: A037092 A037093 A037094 * A037096 A037097 A037098

Keyword

nonn,base

Author

Antti Karttunen, Jan 28 1999. Entry revised Dec 29 2007.

Extensions

More terms from Sean A. Irvine, Dec 08 2020

Status

approved