A297158 Ludic ladder sequence: a(n) = Sum_{k=1..n} (-1)^LudicPi(k), where LudicPi(n) = A192512(n)-1 gives the number of Ludic numbers > 1 and <= n.

0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 4, 3, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 1, 0, -1, -2, -1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, -1, -2, -1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

Offset

0,5

Comments

This is an analogous sequence to A065358, but involving Ludic numbers (A003309) instead of primes. Compare the scatter-plots.

Links

Antti Karttunen, Table of n, a(n) for n = 0..10000

Discussion of SeqFan-list, February 2018.

Index entries for sequences generated by sieves

Formula

a(n) = Sum_{k=1..n} (-1)^(A192512(k)-1).

Prog

(Scheme, with memoization-macro definec)
(definec (A297158 n) (if (zero? n) n (+ (expt -1 (+ -1 (A192512 n))) (A297158 (- n 1)))))

Crossrefs

Cf. A003309, A192512.

Differs from A065358 for the first time at n=19, where a(19) = 3, while A065358(19) = 5.

Sequence in context: A053646 A080776 A360659 * A065358 A062329 A022958

Adjacent sequences: A297155 A297156 A297157 * A297159 A297160 A297161

Keyword

sign

Author

Antti Karttunen, Feb 22 2018

Status

approved