

A260735


Iterates of A234742, starting from value a(0) = 455, with a(1) = A234742(a(0)), a(2) = A234742(a(1)), etc.


8



455, 3087, 24843, 72975, 332563, 602919, 5893875, 221402727, 322063831, 5853742587, 10696444275, 75642464331, 749833439355, 1724537517955, 2295761459035, 4498164915283, 9436077956619, 369311889576231, 10610033249983167, 135786986032294135, 460149860040811083, 2879918014301480295, 63102417694969716063, 339029616686070752991
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OFFSET

0,1


COMMENTS

455 is the first term of A236844 that doesn't settle to a fixed point at least for the first 2000 iterations of A234742. Cf. also A260713.


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..100


FORMULA

a(0) = 455; for n >= 1, a(n) = A234742(a(n1)).


EXAMPLE

The initial value a(0) = 455 ("111000111" in binary) encodes polynomial (with coefficients 0 or 1) x^8 + x^7 + x^6 + x^2 + x + 1, which in ring GF(2)[X] factorizes as (x + 1)(x + 1)(x^2 + x + 1)(x^2 + x + 1)(x^2 + x + 1). (x+1) is encoded by 3 ("11" in binary) and (x^2 + x + 1) by 7 ("111" in binary). Multiplying 3*3*7*7*7 yields the next term of the sequence, thus a(1) = 3087.
3087 ("110000001111" in binary) in turn encodes polynomial x^11 + x^10 + x^3 + x^2 + x + 1 which factorizes as (x + 1)(x^2 + x + 1)(x^2 + x + 1)(x^3 + x^2 + 1)(x^3 + x^2 + 1). Polynomial (x^3 + x^2 + 1) is encoded by 13, as 13 is "1101" in binary. Multiplying 3*7*7*13*13 yields the next term of the sequence, a(2) = 24843.


PROG

(PARI)
allocatemem((2^30));
A234742(n) = factorback(subst(lift(factor(Mod(1, 2)*Pol(binary(n)))), x, 2)); \\ After M. F. Hasler's Feb 18 2014 code.
iterates_of_A234742(start, filename) = {my(n=start, prev=1, prevprev=1, i=0); until((n==prevprev), write(filename, i, " ", n); prevprev = prev; prev = n; n = A234742(n); i++)} \\ Computes bfile up to the second occurrence of the fixed point or until the user presses CtrlC.
iterates_of_A234742(455, "b260735.txt")
(Scheme, with memoizing macro definec)
(definec (A260735 n) (if (zero? n) 455 (A234742 (A260735 ( n 1)))))


CROSSREFS

Cf. A234742, A260712, A260713.
Cf. A260719 (for each term, gives the number of irreducible factors in ring GF(2)[X] for the corresponding encoded polynomial, equal to how many numbers are multiplied together at each step).
Subsequence of A004767.
Cf. also A244323, A260729, A260441 for iterations starting from other values.
Sequence in context: A123563 A043475 A324633 * A241618 A251337 A282232
Adjacent sequences: A260732 A260733 A260734 * A260736 A260737 A260738


KEYWORD

nonn


AUTHOR

Antti Karttunen, Aug 04 2015


STATUS

approved



