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A260441
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Iterates of A234742, starting from value a(0) = 1361, with a(1) = A234742(a(0)), a(2) = A234742(a(1)), etc.
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8
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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
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0,1
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COMMENTS
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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.
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LINKS
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FORMULA
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a(0) = 1361; for n >= 1, a(n) = A234742(a(n-1)).
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EXAMPLE
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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.
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PROG
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(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)
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CROSSREFS
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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).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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