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A260426
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a(1) = 1, a(A206074(n)) = A014580(a(n)), a(A205783(1+n)) = A091242(a(n)), where A014580 [respectively A091242] give binary codes for irreducible [resp. reducible] polynomials over GF(2), while A206074 and A205783 give similar codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.
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8
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1, 2, 3, 4, 7, 5, 11, 6, 8, 12, 25, 9, 13, 17, 10, 14, 47, 18, 19, 34, 15, 20, 31, 24, 55, 16, 21, 62, 137, 26, 37, 27, 45, 22, 28, 42, 59, 33, 71, 23, 87, 29, 41, 79, 166, 35, 61, 49, 36, 58, 30, 38, 319, 54, 91, 76, 44, 89, 97, 32, 203, 108, 39, 53, 99, 200, 67, 46, 103, 78, 185, 64, 131, 48, 75, 40, 379, 50, 73, 373, 109, 70, 433, 113, 95, 57, 1123, 111, 143, 121
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OFFSET
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1,2
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COMMENTS
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Each term of A260427 resides in a separate infinite cycle. This follows because any polynomial with (coefficients 0 or 1) that is irreducible over GF(2) is also irreducible over Q, in other words, A014580 is a subset of A206074. [See Thomas Ordowski's Feb 21 2014 comment in A014580] and thus any term of A091242 in A206074 is trapped into a trajectory containing only terms of A014580.
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LINKS
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FORMULA
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As a composition of related permutations:
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PROG
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(PARI)
allocatemem(234567890);
vecsize = (2^24)-4;
uplim = 2^25;
v014580 = vector(vecsize); A014580 = n -> v014580[n];
v091242 = vector(vecsize); A091242 = n -> v091242[n];
v255574 = vector(vecsize); A255574 = n -> v255574[n];
isA206074(n) = polisirreducible(Pol(binary(n)));
v255574[1] = 0; i=0; j=0; n=2; while((n < uplim), if(!(n%65536), print1(n, ", ")); v255574[n] = v255574[n-1]+A257000(n); if(isA014580(n), i++; v014580[i] = n, j++; v091242[j] = n); n++); print(n);
for(n=1, 7968, write("b260426.txt", n, " ", A260426(n)));
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CROSSREFS
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Differs from A245703 for the first time at n=25, where a(25)=55, while A245703(25)=16.
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KEYWORD
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AUTHOR
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STATUS
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approved
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