A064494 Shotgun (or Schrotschuss) numbers: limit of the recursion B(k) =T[k](B(k-1)), where B(1) = (1,2,3,4,5,...) and T[k] is the Transformation that permutes the entries k(2i-1) and k(2i) for all positive integers i.

1, 4, 8, 6, 12, 14, 16, 9, 18, 20, 24, 26, 28, 22, 39, 15, 36, 35, 40, 38, 57, 34, 48, 49, 51, 44, 46, 33, 60, 77, 64, 32, 75, 56, 81, 68, 76, 58, 100, 55, 84, 111, 88, 62, 125, 70, 96, 91, 98, 95, 134, 72, 108, 82, 141, 80, 140, 92, 120, 156, 124, 94, 121, 52, 152, 145

Offset

1,2

Comments

Sequence is prime-free.

Links

Table of n, a(n) for n=1..66.

K. Strassburger, Plot of shotgun numbers

Example

B(1) = 1,2,3,4,5,6,7,8, 9,10,11,12,13,14,...
B(2) = 1,4,3,2,5,8,7,6, 9,12,11,10,13,16,...
B(3) = 1,4,8,2,5,3,7,6,10,12,11, 9,13,16,...
B(4) = 1,4,8,6,5,3,7,2,10,12,11,14,13,16,...

Mathematica

max = 66; b[1, j_] := j; b[k_, j_] := b[k, j] = b[k-1, j]; Do[b[k, 2j*k-k] = b[k-1, 2j*k]; b[k, 2j*k] = b[k-1, 2j*k-k], {k, 2, max}, {j, 1, max}]; a[n_] := b[max, n]; Table[a[n], {n, 1, max}] (* Jean-François Alcover, Oct 11 2012 *)

Prog

(SageMath)
def divsign(s, k):
    if not k.divides(s): return 0
    return (-1)^(s//k)*k
def A064494(n):
    s = n
    for k in srange(n, 1, -1):
        s -= divsign(s, k)
    return s
print([A064494(n) for n in (1..66)]) # Peter Luschny, Sep 16 2019

Crossrefs

Cf. A064728, A064590, A064627.

Sequence in context: A328278 A288189 A335159 * A119800 A330685 A063723

Adjacent sequences: A064491 A064492 A064493 * A064495 A064496 A064497

Keyword

nice,nonn

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 16 2001

Status

approved