A260735 Iterates of A234742, starting from value a(0) = 455, with a(1) = A234742(a(0)), a(2) = A234742(a(1)), etc.

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

Offset: 0

Author

Antti Karttunen, Aug 04 2015

Keywords

• nonn

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.

Examples

			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.
		

Links

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

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.

Programs

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)))))

Formula

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