The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A305300 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A305300

Ordinal transform of A305430, the smallest k > n whose binary expansion encodes an irreducible (0,1)-polynomial over Q.
(history; published version)

#15 by Joerg Arndt at Mon Dec 20 09:49:17 EST 2021

STATUS

reviewed

approved

#14 by Michel Marcus at Mon Dec 20 08:18:06 EST 2021

STATUS

proposed

reviewed

#13 by Jean-François Alcover at Mon Dec 20 08:17:49 EST 2021

STATUS

editing

proposed

#12 by Jean-François Alcover at Mon Dec 20 08:17:44 EST 2021

MATHEMATICA

binPol[n_, x_] := With[{bb = IntegerDigits[n, 2]}, bb.x^Range[Length[bb]-1, 0, -1]];

ip[n_] := If[IrreduciblePolynomialQ[binPol[n, x]], 1, 0];

A305430[n_] := Module[{k = n + 1}, While[ip[k] == 0, k++]; k];

b[_] = 0;

a[n_] := a[n] = With[{t = A305430[n]}, b[t] = b[t]+1];

Array[a, 105] (* Jean-François Alcover, Dec 20 2021 *)

STATUS

approved

editing

#11 by Susanna Cuyler at Sat Jun 09 19:00:21 EDT 2018

STATUS

proposed

approved

#10 by Antti Karttunen at Sat Jun 09 16:59:34 EDT 2018

STATUS

editing

proposed

#9 by Antti Karttunen at Sat Jun 09 16:45:07 EDT 2018

CROSSREFS

Cf. A257000, A305429, A305430, A305437, A305438.

#8 by Antti Karttunen at Sat Jun 09 13:02:54 EDT 2018

PROG

A257000(n) = polisirreducible(Pol(binary(n)));

#7 by Antti Karttunen at Sat Jun 09 13:02:00 EDT 2018

NAME

Ordinal transform of A305430, the smallest k > n whose binary expansion encodes an irreducible (0,1)-polynomial over Q.

#6 by Antti Karttunen at Sat Jun 09 13:00:22 EDT 2018

LINKS

Antti Karttunen, <a href="/A305300/b305300.txt">Table of n, a(n) for n = 1..65537</a>

CROSSREFS

Cf. A206074 (gives the positions of other 1's after the initial one).