A260441 Iterates of A234742, starting from value a(0) = 1361, with a(1) = A234742(a(0)), a(2) = A234742(a(1)), etc.

1361, 3721, 8073, 40257, 64125, 344925, 1121373, 4127085, 47053305, 89025909, 256718241, 864417085, 2339944761, 7793372565, 10483463769, 15540712857, 19217417625, 51731153357, 315005744053, 731886242745, 3047881618969, 19546038155241, 55232813508469, 389828042124021, 1225948485247905, 17008166929275225

Offset: 0

Author

Antti Karttunen, Aug 04 2015

Keywords

• nonn

Comments

1361 is the first term of A091209 that doesn't reach a fixed point at least for the first 2000 iterations of A234742. Cf. also A260716.

Note that 1361 = A048720(61,61).

Examples

			61 ("111101" in binary) = A014580(14), i.e., it encodes the fourteenth polynomial with coefficients 0 or 1 that is irreducible over GF(2), namely x^5 + x^4 + x^3 + x^2 + 1. When we multiply that polynomial by itself (in ring GF(2)[X]), we get x^10 + x^8 + x^6 + x^4 + 1, encoded by 1361 with binary representation "10101010001" [1361 = A048720(61,61)]. This is used as the initial value a(0) of this sequence. The next term is obtained by multiplying these two factors 61 and 61 as ordinary integers, which gives a(1) = 61*61 = 3721.
3721 ("111010001001" in binary) in turn encodes polynomial x^11 + x^10 + x^9 + x^7 + x^3 + 1 which factorizes in ring GF(2)[X] as (x + 1)(x + 1)(x + 1)(x^8 + x^5 + x^3 + x + 1). Polynomial (x + 1) is encoded by 3 ("11" in binary) and (x^8 + x^5 + x^3 + x + 1) by 299 ("100101011" in binary). Multiplying 3*3*3*299 in ordinary way gives the next term of the sequence, a(2) = 8073.
		

Links

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

Crossrefs

Cf. A014580, A048720, A234742, A260712, A260713, A260716.

Cf. A260720 (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 the next step).

Subsequence of A016813.

Cf. also A244323, A260729, A260735 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(1361, "b260441.txt")

Scheme

;; With memoizing macro definec.
(definec (A260441 n) (if (zero? n) 1361 (A234742 (A260441 (- n 1)))))

Formula

a(0) = 1361; for n >= 1, a(n) = A234742(a(n-1)).