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A305300 Ordinal transform of A305430, the smallest k > n whose binary expansion encodes an irreducible (0,1)-polynomial over Q. 3
1, 1, 1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 1, 2, 1, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(1) = 1; for n > 1, if A257000(n) = 1 [when n is in A206074], a(n) = 1, otherwise a(n) = 1 + n - A305429(n).

PROG

(PARI)

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

A305429(n) = if(n<3, 1, my(k=n-1); while(k>1 && !A257000(k), k--); (k));

A305300(n) = if((1==n)||(1==A257000(n)), 1, 1+(n-A305429(n)));

(PARI)

up_to = 65537;

ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };

A305430(n) = { my(k=1+n); while(!A257000(k), k++); (k); };

v305300 = ordinal_transform(vector(up_to, n, A305430(n)));

A305300(n) = v305300[n];

CROSSREFS

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

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

Cf. also A175851.

Sequence in context: A161296 A161271 A160975 * A330241 A175851 A049711

Adjacent sequences:  A305297 A305298 A305299 * A305301 A305302 A305303

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 09 2018

STATUS

approved

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Last modified October 23 14:42 EDT 2021. Contains 348214 sequences. (Running on oeis4.)