

A293229


a(0) = 0; and for n > 0, a(n) = a(n1) + (A008966(4n+3)  A008966(4n+1)).


3



0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 3, 4, 4, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 4, 4, 4, 3, 2, 2, 2, 3, 3, 4, 4, 4, 4, 3, 3, 3, 4, 4, 5, 5, 4, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2
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OFFSET

0,12


COMMENTS

The sequence indicates about a possible bias (or lack of it) in the distribution of squarefree numbers among the numbers of the form 4k+1 vs. the numbers of the form 4k+3. See A293429 for another version.
The first negative term is a(1702) = 1.


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10000
Hans Havermann, Plot of n, a(n) for n = 0..200000
Hans Havermann, Plot of n, a(n) for n = 0..10^7


FORMULA

a(0) = 0; and for n > 0, a(n) = a(n1) + (A008966(4n+3)  A008966(4n+1)).


PROG

(PARI) up_to = 10000; bias = 0; for(k=0, up_to, bias += (issquarefree((4*k)+3)issquarefree((4*k)+1)); write("b293229.txt", k, " ", bias));
(Scheme, with memoizationmacro definec)
(definec (A293229 n) (if (zero? n) n (+ ( (A008966 (+ 3 (* 4 n))) (A008966 (+ 1 (* 4 n)))) (A293229 ( n 1)))))


CROSSREFS

Cf. A008966, A293428, A293429 (a variant).
Sequence in context: A128080 A062187 A031283 * A185437 A210681 A096520
Adjacent sequences: A293226 A293227 A293228 * A293230 A293231 A293232


KEYWORD

sign


AUTHOR

Antti Karttunen, Oct 12 2017


STATUS

approved



