The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A091203 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A091203

Factorization-preserving isomorphism from binary codes of GF(2) polynomials to integers.
(history; published version)

#26 by Susanna Cuyler at Sun Jun 10 21:14:06 EDT 2018

STATUS

proposed

approved

#25 by Antti Karttunen at Sun Jun 10 15:54:00 EDT 2018

STATUS

editing

proposed

#24 by Antti Karttunen at Sun Jun 10 11:58:26 EDT 2018

FORMULA

A046523(a(n)) = A278233(n).

CROSSREFS

Cf. also A000005, A000040, A001221, A001222, A004247, A008683, A010051, A014580, A048720, A049084, A066247, A091219, A091220, A091221, A091222, A091225, A091227, A091247, A234741, A234742, A245703, A245704, A278233.

#23 by Antti Karttunen at Sun Jun 10 10:11:13 EDT 2018

FORMULA

a(n) = A005940(1+A305418(n)) = A163511(A305428(n)).

CROSSREFS

Cf. also A302024, A302026, A305418, A305428 for other similar permutations.

#22 by Antti Karttunen at Sun Jun 10 10:07:35 EDT 2018

FORMULA

a(n) = A163511(A305428(n))

#21 by Antti Karttunen at Sun Jun 10 07:05:04 EDT 2018

FORMULA

For n <= 1, a(n) = n, for n > 1, a(n) = 2*a(n/2) if n is even, and if n is odd, then a(n) = A003961(A091203a(A305422(n))).

#20 by Antti Karttunen at Sun Jun 10 07:04:21 EDT 2018

FORMULA

From Antti Karttunen, Jun 10 2018: (Start)

For n <= 1, a(n) = n, for n > 1, a(n) = 2*a(n/2) if n is even, and if n is odd, then a(n) = A003961(A091203(A305422(n))).

(End)

PROG

(PARI)

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961

A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));

A305419(n) = if(n<3, 1, my(k=n-1); while(k>1 && !A091225(k), k--); (k));

A305422(n) = { my(f = subst(lift(factor(Pol(binary(n))*Mod(1, 2))), x, 2)); for(i=1, #f~, f[i, 1] = Pol(binary(A305419(f[i, 1])))); fromdigits(Vec(factorback(f))%2, 2); };

A091203(n) = if(n<=1, n, if(!(n%2), 2*A091203(n/2), A003961(A091203(A305422(n))))); \\ Antti Karttunen, Jun 10 2018

STATUS

approved

editing

#19 by Bruno Berselli at Tue Jun 16 06:16:57 EDT 2015

STATUS

reviewed

approved

#18 by Michel Marcus at Mon Jun 15 17:14:30 EDT 2015

STATUS

proposed

reviewed

#17 by Pontus von Brömssen at Mon Jun 15 15:27:18 EDT 2015

STATUS

editing

proposed