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

Author

Antti Karttunen, Feb 22 2018

Keywords

• sign

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

Crossrefs

Cf. A003309, A192512.

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

Formula

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