A234751 -id:A234751 - cp's OEIS frontend

A234747 Self-inverse and multiplicative permutation of natural numbers, A091202-conjugate of Blue code: a(n) = A091203(A193231(A091202(n))).

0, 1, 3, 2, 9, 5, 6, 11, 27, 4, 15, 7, 18, 13, 33, 10, 81, 19, 12, 17, 45, 22, 21, 37, 54, 25, 39, 8, 99, 43, 30, 41, 243, 14, 57, 55, 36, 23, 51, 26, 135, 31, 66, 29, 63, 20, 111, 59, 162, 121, 75, 38, 117, 61, 24, 35, 297, 34, 129, 47, 90, 53, 123, 44, 729

Offset: 0

Antti Karttunen, Dec 31 2013

a(n) has the same prime signature as n: the permutation maps primes to primes, squares to squares, cubes to cubes, and so on.

			Example of multiplicativity: a(7)=11, a(23)=37, a(7*23) = a(161) = a(7)*a(23) = 11*37 = 407.

Cf. A091202, A091203, A193231, A234751.

See A234748 for a variant.

(define (A234747 n) (A091203 (A193231 (A091202 n))))

a(n) = A091203(A193231(A091202(n))).

Completely multiplicative with p_i = p_{A234751(i)} (where p_i stands for the i-th prime, A000040(i)), and a(x*y) = a(x)*a(y) for x, y > 0.

A234746 Self-inverse permutation of integers induced by the restriction of blue-code to reducible polynomials over GF(2): a(n) = A091246(A193231(A091242(n))).

Original entry on oeis.org

2, 1, 3, 9, 8, 7, 6, 5, 4, 11, 10, 12, 13, 14, 16, 15, 22, 21, 20, 19, 18, 17, 39, 38, 36, 37, 42, 41, 40, 46, 48, 47, 44, 43, 45, 25, 26, 24, 23, 29, 28, 27, 34, 33, 35, 30, 32, 31, 68, 67, 69, 63, 64, 66, 65, 72, 71, 70, 76, 75, 73, 74, 52, 53, 55, 54, 50, 49, 51, 58, 57, 56, 61, 62, 60, 59

Offset: 1

Antti Karttunen, Feb 15 2014

nonn

Fixed points: A234749.

Cf. A193231, A091242, A091246, A234745, A234751.

(define (A234746 n) (A091246 (A234745 n)))

a(n) = A091246(A234745(n)) = A091246(A193231(A091242(n))).

A234750 Blue-code restricted to irreducible polynomials over GF(2): a(n) = A193231(A014580(n)).

Original entry on oeis.org

3, 2, 7, 13, 11, 19, 31, 25, 55, 61, 59, 37, 47, 41, 87, 91, 67, 73, 103, 97, 109, 117, 115, 253, 241, 247, 239, 229, 203, 193, 211, 213, 171, 167, 185, 191, 157, 145, 137, 143, 131, 285, 283, 319, 313, 301, 299, 351, 333, 357, 355, 361, 375, 369, 379, 505, 499, 501

Offset: 1

Antti Karttunen, Feb 12 2014

The polynomials are encoded as the number whose binary representation is given by the coefficients of the polynomial, e.g., 13 = 2^3 + 2^2 + 2^0 = 1101_2 encodes 1*X^3 + 1*X^2 + 0*X^1 + 1*X^0 = X^3 + X^2 + 1. - Peter Munn, Apr 28 2021

			From _Peter Munn_, Apr 23 2021: (Start)
Table for polynomials of degree less than 6:
   n   A014580   a(n)   Previous 2 columns
          (n)               in binary
   1       2       3         10       11
   2       3       2         11       10
   3       7       7        111      111
   4      11      13       1011     1101
   5      13      11       1101     1011
   6      19      19      10011    10011
   7      25      31      11001    11111
   8      31      25      11111    11001
   9      37      55     100101   110111
  10      41      61     101001   111101
  11      47      59     101111   111011
  12      55      37     110111   100101
  13      59      47     111011   101111
  14      61      41     111101   101001
(End)

Cf. A234751, A193231, A014580.

(define (A234750 n) (A193231 (A014580 n)))

a(n) = A193231(A014580(n)).

A234749 Fixed points of permutation A234746.

Original entry on oeis.org

3, 12, 13, 14, 85, 86, 87, 96, 97, 102, 103, 216, 217, 218, 219, 230, 231, 236, 237, 308, 313, 314, 323, 324, 325, 1370, 1371, 1372, 1373, 1382, 1383, 1388, 1389, 1446, 1447, 1452, 1453, 1464, 1465, 1466, 1467, 1600, 1601, 1606, 1615, 1616, 1617, 1678, 1679, 1680, 1691, 1692, 1697, 1698

Offset: 1

Antti Karttunen, Feb 15 2014

nonn

A234752 gives the corresponding binary encodings for those reducible GF(2)[X] polynomials that are fixed by blue code (A193231).

Fixed points of A234751 seem to be rarer. The first 22 values are: 3, 6, 21, 52, 55, 200, 203, 212, 461, 462, 479, 480, 483, 2150, 2151, 2176, 2177, 2190, 2195, 2208, 2209, 2214.

Antti Karttunen, Table of n, a(n) for n = 1..232

Cf. A234746, A234752, A193231, A118666.

cp's OEIS Frontend

A234747 Self-inverse and multiplicative permutation of natural numbers, A091202-conjugate of Blue code: a(n) = A091203(A193231(A091202(n))).

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A234746 Self-inverse permutation of integers induced by the restriction of blue-code to reducible polynomials over GF(2): a(n) = A091246(A193231(A091242(n))).

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A234750 Blue-code restricted to irreducible polynomials over GF(2): a(n) = A193231(A014580(n)).

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A234749 Fixed points of permutation A234746.

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