A226569 -id:A226569 - cp's OEIS frontend

A226532 If n = Product_{i>0} prime(i)^e(i), then a(n) = Product_{i>0} prime(i)^(XOR_{j>=i} e(j)), where XOR is bitwise XOR.

1, 2, 6, 4, 30, 3, 210, 8, 36, 15, 2310, 24, 30030, 105, 5, 16, 510510, 72, 9699690, 120, 35, 1155, 223092870, 12, 900, 15015, 216, 840, 6469693230, 10, 200560490130, 32, 385, 255255, 7, 9, 7420738134810, 4849845, 5005, 60, 304250263527210, 70, 13082761331670030, 9240, 1080, 111546435, 614889782588491410

Offset: 1

Paul Tek, Jun 10 2013

nonn

This sequence is a permutation of the natural numbers.
The powers of 2 are the fixed points of this sequence.
a(prime(i)) = A002110(i) for any i > 0.
a(i^2) = a(i)^2 for any i > 0.
a(A019565(n)) = A019565(A006068(n)) for any n >= 0.

			a(50) = a(2^1 * 3^0 * 5^2)
      = 2^xor(1,0,2) * 3^xor(0,2) * 5^xor(2)
      = 2^3          * 3^2        * 5^2
      = 1800.

Paul Tek, Table of n, a(n) for n = 1..2370
Paul Tek, PERL program for this sequence
Index entries for sequences that are permutations of the natural numbers

Cf. A006068.

Cf. A226569 (inverse), A067255, A000040.

import Data.Bits (xor)
a226532 n = product $ zipWith (^)
            a000040_list (scanr1 xor $ a067255_row n :: [Integer])
-- Reinhard Zumkeller, Jun 11 2013

Perl
```
# See Tek link.
```

A225607 If the run lengths of the binary representation of n are [1+r_1, 1+r_2, 1+r_3, ..., 1+r_k], then those of a(n) are [1+(r_1), 1+(r_1 XOR r_2), 1+(r_2 XOR r_3), ..., 1+(r_{k-1} XOR r_k)], where XOR denotes the XOR binary operator.

Original entry on oeis.org

1, 2, 3, 4, 5, 12, 7, 8, 19, 10, 11, 6, 25, 56, 15, 16, 71, 38, 9, 20, 21, 44, 23, 48, 27, 50, 51, 112, 113, 240, 31, 32, 271, 142, 143, 76, 77, 36, 79, 40, 83, 42, 43, 22, 89, 184, 47, 24, 391, 54, 13, 100, 101, 204, 103, 14, 451, 226, 227, 120, 481, 992, 63

Offset: 1

Paul Tek, Aug 06 2013

Inverse permutation of A227987.

			For n=28927:
(1) binary representation of n = "111000011111111",
(2) run lengths of n = [1+2,1+3,1+7],
(3) run lengths of a(n) = [1+2,1+(2 XOR 3),1+(3 XOR 7)]=[3,2,5],
(4) binary representation of a(n) = "1110011111",
(5) a(n) = 927.

Paul Tek, Table of n, a(n) for n = 1..10000
Paul Tek, PERL program for this sequence
Index entries for sequences that are permutations of the natural numbers

Cf. A227987, A226569.

Perl
```
See Link section.
```

cp's OEIS Frontend

A226532 If n = Product_{i>0} prime(i)^e(i), then a(n) = Product_{i>0} prime(i)^(XOR_{j>=i} e(j)), where XOR is bitwise XOR.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Perl