A372297 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, if k is prime.

1, 4, 8, 2, 12, 3, 16, 6, 10, 5, 24, 9, 28, 7, 18, 14, 36, 15, 40, 20, 26, 11, 48, 21, 27, 13, 32, 22, 60, 25, 64, 30, 42, 17, 39, 33, 76, 19, 50, 35, 84, 38, 88, 34, 52, 23, 96, 45, 54, 46, 66, 44, 108, 51, 63, 49, 74, 29, 120, 55, 124, 31, 65, 62, 75

Offset: 1

Author

Jennifer Buckley, Apr 25 2024

Keywords

• nonn

Comments

Sequence contains all positive integers.

a(2p) = p for all prime numbers p.

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) = 1,4,8,2, 5,3,7,6,10,12,11, 9,13,16,... (No change)
B(5) = 1,4,8,2,12,3,7,6,10, 5,11, 9,13,16,...
		

Links

• Jennifer Buckley, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A064494.

Programs

Mathematica

max = 66; b[1, j_] := j; b[k_, j_] := b[k, j] = b[k-1, j]; Do[If[PrimeQ[k],b[k, 2j*k-k] = b[k-1, 2j*k]; b[k, 2j*k] = b[k-1, 2j*k-k],b[k,j ]=b[k-1,j]], {k, 2, max}, {j, 1, max}]; a[n_] := b[max, n]; Table[a[n], {n, 1, max}]