login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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(n-1)).

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 b-file up to the second occurrence of the fixed point or until the user presses Ctrl-C.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 24 03:20 EDT 2019. Contains 326260 sequences. (Running on oeis4.)