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A260720 a(n) = A091222(A260441(n)): number of irreducible factors (in ring GF(2)[X]) of the binary encoded polynomial obtained after the n-th iteration of A234742, when starting with the initial value 1361. 3
2, 4, 5, 2, 6, 4, 4, 8, 3, 3, 4, 3, 3, 3, 2, 2, 3, 5, 2, 4, 7, 2, 5, 3, 7, 3, 3, 4, 4, 7, 4, 6, 5, 3, 2, 5, 6, 4, 8, 4, 4, 6, 3, 4, 5, 3, 3, 4, 5, 6, 6, 6, 3, 6, 10, 6, 4, 5, 6, 8, 3, 3, 5, 3, 8, 2, 3, 4, 5, 6, 5, 4, 5, 5, 7, 4, 5, 6, 3, 5, 6, 5, 6, 7, 3, 8, 7, 10, 7, 9, 6, 5, 2, 6, 5, 7, 6, 8, 6, 3, 10, 3, 9, 8, 6, 6, 5, 8, 6, 7, 3, 6, 8, 5, 5, 5, 8, 5, 6, 5, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Records occur in positions 0, 1, 2, 4, 7, 54, 139, 174, 225, 398, 778, and they are 2, 4, 5, 6, 8, 10, 11, 13, 16, 20, 21.

First 2's occur at positions 0, 3, 14, 15, 18, 21, 34, 65, 92, 135, 200, 255, 339, 362, 468, 511, 825, 1042, 1809.

Note that if this sequence ever obtains value 1, then the rest of terms are also 1's, as then A260441 has attained as its constant value one of the terms of A091214 (which is a subsequence of A235035, the fixed points of A234742).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..2049

FORMULA

a(n) = A091222(A260441(n)).

EXAMPLE

See example in A260441. This sequence gives the number of those irreducible factors, counted with multiplicity. For example, a(0) = 2 (for 61 * 61), a(1) = 4 (for 3 * 3 * 3 * 299). Note that irreducibility here refers to irreducibility in ring GF(2)[X], as for example 299 = 13*23 when factored to ordinary primes.

PROG

(PARI)

allocatemem((2^30));

{my(n=1361, fm); for(i=0, 2049, fm=factor(Pol(binary(n))*Mod(1, 2)); write("b260720.txt", i, " ", sum(k=1, #fm~, fm[k, 2])); n = factorback(subst(lift(fm), x, 2))); };

(Scheme) (define (A260720 n) (A091222 (A260441 n)))

CROSSREFS

Cf. A091214, A091222, A234742, A235035, A260441, A260719.

Sequence in context: A234350 A324035 A096352 * A197587 A231729 A071286

Adjacent sequences:  A260717 A260718 A260719 * A260721 A260722 A260723

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 04 2015

STATUS

approved

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Last modified August 21 05:48 EDT 2019. Contains 326162 sequences. (Running on oeis4.)