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A107079 Minimal number of squared primes in a squarefree gap of length n. 4
1, 2, 3, 4, 4, 5, 6, 7, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 13, 14, 14, 15, 16, 17, 17, 17, 18, 18, 18, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 30, 30, 30, 31, 32, 32, 32, 32, 33, 33, 34, 34, 35, 35, 36, 37, 38, 38, 39, 40, 40, 40, 41, 42, 43, 43, 44, 45, 46, 46, 47 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

Louis Marmet, First occurrences of squarefree gaps and an algorithm for their computation

L. Marmet, First occurrences of square-free gaps and an algorithm for their computation, arXiv preprint arXiv:1210.3829 [math.NT], 2012. - From N. J. A. Sloane, Jan 01

FORMULA

a(n) = sum{k=0..n-1, moebius_mu(n-k-1) mod 2}.

a(n) = A013928(n+1) + A107078(n).

From Antti Karttunen, Oct 07 2016: (Start)

a(n) = 1 + A013928(n). [Cf. Charles R Greathouse IV's PARI-program.]

For all n >= 1, a(A005117(n)) = n.

(End)

MATHEMATICA

a[n_] := Sum[Boole[SquareFreeQ[k]], {k, 1, n-1}] + 1;

Array[a, 100] (* Jean-Fran├žois Alcover, Sep 11 2018, from A013928 *)

PROG

(PARI) A107079(n)=1+sum(k=1, n-1, bitand(moebius(k), 1)) \\ Charles R Greathouse IV, Sep 22 2008

CROSSREFS

One more than A013928. A left inverse of A005117.

Cf. A045882, A107078.

Sequence in context: A306890 A116549 A268382 * A025528 A255338 A123580

Adjacent sequences:  A107076 A107077 A107078 * A107080 A107081 A107082

KEYWORD

nonn

AUTHOR

Paul Barry, May 10 2005

EXTENSIONS

New definition from Charles R Greathouse IV, Sep 22 2008

STATUS

approved

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Last modified August 24 16:21 EDT 2019. Contains 326295 sequences. (Running on oeis4.)