

A260441


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


8



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
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OFFSET

0,1


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).


LINKS

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


FORMULA

a(0) = 1361; for n >= 1, a(n) = A234742(a(n1)).


EXAMPLE

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.


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(1361, "b260441.txt")
(Scheme, with memoizing macro definec)
(definec (A260441 n) (if (zero? n) 1361 (A234742 (A260441 ( n 1)))))


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.
Sequence in context: A023091 A242458 A223254 * A265498 A113507 A119521
Adjacent sequences: A260438 A260439 A260440 * A260442 A260443 A260444


KEYWORD

nonn


AUTHOR

Antti Karttunen, Aug 04 2015


STATUS

approved



