A255574 a(n) = Number of terms of A206074 in range 0 .. n.

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

Offset: 0

Author

Antti Karttunen, May 14 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Partial sums of A257000.

Cf. A000720, A014580, A091226, A206074, A255572, A255573.

Programs

Mathematica

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 *)

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)))))

Formula

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.]