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A255574
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a(n) = Number of terms of A206074 in range 0 .. n.
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9
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0, 0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 26, 26, 27, 27
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 0..65537
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FORMULA
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a(0) = 0; for n >= 1, a(n) = A257000(n) + a(n-1).
Other identities and observations.
For all n >= 0:
a(n) = n - A255573(n).
For all n >= 1:
a(A206074(n)) = n. [This sequence works as a left inverse for injection A206074.]
a(n) >= A000720(n). [Because primes is a subsequence of A206074.]
a(n) >= A091226(n). [Because A014580 is a subsequence of A206074.]
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MATHEMATICA
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binPol[n_, x_] := With[{bb = IntegerDigits[n, 2]}, bb.x^Range[Length[bb]-1, 0, -1]];
b[n_] := If[IrreduciblePolynomialQ[binPol[n, x]], 1, 0];
b /@ Range[0, 128] // Accumulate (* Jean-François Alcover, Dec 20 2021 *)
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PROG
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(PARI)
isA206074(n) = polisirreducible(Pol(binary(n)));
A255574_write_bfile(up_to_n) = { my(n, a_n=0); for(n=0, up_to_n, if(isA206074(n), a_n++); write("b255574.txt", n, " ", a_n)); };
A255574_write_bfile(65537);
(Scheme) (definec (A255574 n) (if (zero? n) n (+ (A257000 n) (A255574 (- n 1)))))
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CROSSREFS
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Partial sums of A257000.
Cf. A000720, A014580, A091226, A206074, A255572, A255573.
Sequence in context: A000720 A230980 A070549 * A283992 A074796 A061070
Adjacent sequences: A255571 A255572 A255573 * A255575 A255576 A255577
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, May 14 2015
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STATUS
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approved
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