A249990 -id:A249990 - cp's OEIS frontend

A252448 Inverse permutation to A249990.

2, 1, 4, 5, 7, 3, 9, 8, 11, 12, 18, 6, 13, 14, 16, 10, 20, 17, 24, 25, 31, 15, 26, 19, 22, 23, 33, 32, 39, 27, 29, 21, 35, 34, 37, 40, 50, 30, 41, 42, 48, 38, 52, 49, 60, 61, 71, 28, 43, 44, 46, 36, 54, 47, 62, 63, 69, 45, 64, 51, 58, 59, 73, 72, 83, 53, 56

Offset: 1

Reinhard Zumkeller, Dec 17 2014

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Cf. A249990 (inverse), A252458 (fixed points).

import Data.List (elemIndex); import Data.Maybe (fromJust)
a252448 = (+ 1) . fromJust . (`elemIndex` a249990_list)

A252458 Fixed points of permutations A249990 and A252448.

Original entry on oeis.org

8, 13, 14, 34, 139, 140, 383, 960, 1609, 2064, 5487, 7171, 7715, 21059, 22523, 24148, 91924, 117728, 200193, 304381, 609147, 866933, 920405, 930571, 985939

Offset: 1

Reinhard Zumkeller, Dec 17 2014

nonn

A249990(a(n)) = A252448(a(n)) = a(n).

Cf. A249990, A252448.

a252458 n = a252458_list !! (n-1)
a252458_list = [x | x <- [1..], a249990 x == x]

A249991 Start with the natural numbers, reverse the order in each pair, skip one number, reverse the order in each triple, skip one number, and so on.

Original entry on oeis.org

2, 3, 5, 10, 12, 13, 21, 26, 28, 39, 41, 46, 54, 65, 67, 82, 84, 85, 109, 114, 122, 137, 139, 160, 178, 179, 181, 222, 230, 235, 269, 274, 276, 313, 331, 336, 370, 381, 383, 424, 426, 437, 471, 476, 536, 541, 549, 554, 618, 629, 647, 704, 706, 707, 761, 818

Offset: 1

Alex Ratushnyak, Nov 27 2014

nonn

Start with the natural numbers. Reverse the order of numbers in each pair. Skip one number. In the remainder (that is, "1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11,...") reverse the order in each triple. Skip one number. In the remainder (it starts with "4, 1, 8, 5, 6, 9, 10, 7") reverse the order in each tetrad. Skip one number. And so on.

Cf. A000960, A026239, A249990.

Partial sums of A057031.

TOP = 100000
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]
  print(a[1], end=', ')
  a[1:] = a[2:]

A256964 Solution to Popular Computing Problem 196.

Original entry on oeis.org

6, 8, 10, 9, 14, 12, 4, 15, 22, 5, 26, 21, 18, 32, 34, 7, 38, 40, 24, 33, 46, 27, 50, 39, 30, 56, 58, 11, 62, 48, 36, 51, 70, 13, 74, 57, 42, 60, 82, 45, 86, 88, 16, 69, 94, 17, 98, 75, 54, 104, 106, 19, 110, 84, 20, 87, 118, 63, 122, 93, 66, 128, 130, 23, 134

Offset: 1

N. J. A. Sloane, Apr 16 2015

nonn

See link for statement of the problem.

Alois P. Heinz, 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 196.

Cf. A249990.

A256964 = {}; nlist = Range[3, 2 10^4 + 10]; Do[x = nlist[[i]]; AppendTo[ A256964, nlist[[x+i]]]; nlist[[x+i]] = x, {i, 10^4}]; A256964 (* Jean-François Alcover, May 31 2019, after Chai Wah Wu *)

A256964_list, nlist = [], list(range(3,2*10**4+10))
for i in range(10**4):
    x = nlist[i]
    A256964_list.append(nlist[x+i])
    nlist[x+i] = x # Chai Wah Wu, Apr 16 2015

cp's OEIS Frontend

A252448 Inverse permutation to A249990.

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A252458 Fixed points of permutations A249990 and A252448.

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Haskell

A249991 Start with the natural numbers, reverse the order in each pair, skip one number, reverse the order in each triple, skip one number, and so on.

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A256964 Solution to Popular Computing Problem 196.

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