A249990 Start with the natural numbers, reverse the order in each pair, skip one pair, reverse the order in each triple, skip one triple, and so on.

2, 1, 6, 3, 4, 12, 5, 8, 7, 16, 9, 10, 13, 14, 22, 15, 18, 11, 24, 17, 32, 25, 26, 19, 20, 23, 30, 48, 31, 38, 21, 28, 27, 34, 33, 52, 35, 42, 29, 36, 39, 40, 49, 50, 58, 51, 54, 41, 44, 37, 60, 43, 66, 53, 84, 67, 68, 61, 62, 45, 46, 55, 56, 59, 76, 94, 77, 90

Offset

1,1

Comments

A permutation of natural numbers generated by the following algorithm.

Start with the natural numbers. Reverse the order of numbers in each pair. Skip one pair. In the remainder (that is, "4, 3, 6, 5, 8, 7, 10, 9, 12, 11,...") reverse the order in each triple. Skip one triple. In the remainder (it starts with "7, 8, 5, 12, 9, 10") reverse the order in each tetrad. Skip one tetrad. And so on.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Popular Computing (Calabasas, CA), Problems 195 and 196, Vol. 5 (No. 55, 1977), annotated and scanned copy of page PC55-4. See Problem 195.

Index entries for sequences that are permutations of the natural numbers

Example

Start with:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ...
After the first step:
2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, ...
After the 2nd step:
2, 1, 6, 3, 4, 7, 8, 5, 12, 9, 10, 13, 14, 11, 18, 15, 16, ...
After the 3rd step:
2, 1, 6, 3, 4, 12, 5, 8, 7, 14, 13, 10, 9, 16, 15, 18, 11, ...

Prog

(Python)
TOP = 100
a = list(range(TOP))
for step in range(2, TOP):
    numBlocks = (len(a)-1) // step
    if numBlocks==0:  break
    a = a[:(1+numBlocks*step)]
    for pos in range(1, len(a), step):
        a[pos:pos+step] = a[pos+step-1:pos-1:-1]
    for i in range(1, step+1):  print(str(a[i]), end=', ')
    a[1:] = a[step+1:]
(Haskell)
a249990 n = a249990_list !! (n-1)
a249990_list = f 2 [1..] where
   f k xs = reverse ys ++ f (k + 1) (g zs) where
            g us = reverse vs ++ g ws where
                   (vs, ws) = splitAt k us
            (ys, zs) = splitAt k xs
-- Reinhard Zumkeller, Dec 17 2014

Crossrefs

Cf. A000960, A026239, A249991.

Cf. A252448 (inverse), A252458 (fixed points).

Sequence in context: A124443 A077172 A160047 * A097288 A223894 A308573

Adjacent sequences: A249987 A249988 A249989 * A249991 A249992 A249993

Keyword

nonn

Author

Alex Ratushnyak, Nov 27 2014

Status

approved