

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



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)


CROSSREFS

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).


KEYWORD

nonn


AUTHOR



STATUS

approved



