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

Author

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

Keywords

• nice
• nonn

Comments

Sequence is prime-free.

Examples

			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,...
		

Links

• K. Strassburger, Plot of shotgun numbers

Crossrefs

Cf. A064728, A064590, A064627.

Programs

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 *)

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