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A091205 Deep multiplicative isomorphism from GF(2)[X]-polynomials to integers. +0
11
0, 1, 2, 3, 4, 9, 6, 5, 8, 15, 18, 7, 12, 23, 10, 27, 16, 81, 30, 13, 36, 25, 14, 69, 24, 11, 46, 45, 20, 21, 54, 19, 32, 57, 162, 115, 60, 47, 26, 63, 72, 61, 50, 33, 28, 135, 138, 17, 48, 35, 22, 243, 92, 39, 90, 37, 40, 207, 42, 83, 108, 29, 38, 75, 64, 225, 114, 103 (list; graph; listen)
OFFSET

0,3

COMMENT

This isomorphism can be used in most cases where mere A091203 would work, but in addition this preserves also the structures where we recurse on irreducible polynomial's A014580-index. E.g. we have: A091238(n) = A061775(a(n)). This is possible because the permutation contains an image of itself in its restriction to irreducible polynomials, i.e. a(n) = A049084(a(A014580(n))).

LINKS

A. Karttunen, Scheme-program for computing this sequence.

Index entries for sequences operating on GF(2)[X]-polynomials

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(0)=0, a(1)=1. For n's coding an irreducible polynomial, that is if n=A014580(i), we have a(n) = A000040(a(i)) and for reducible polynomials a(ir_i X ir_j X ...) = a(ir_i) * a(ir_j) * ..., where ir_i = A014580(i), X stands for carryless multiplication of GF(2)[X] polynomials (A048720) and * for the ordinary multiplication of integers (A004247).

CROSSREFS

Inverse: A091204.

Sequence in context: A091203 A106445 A106443 this_sequence A106447 A060866 A064478

Adjacent sequences: A091202 A091203 A091204 this_sequence A091206 A091207 A091208

KEYWORD

nonn

AUTHOR

Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004

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Last modified November 23 17:09 EST 2009. Contains 167438 sequences.


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