A300392 a(1)=1, a(n) = max(sum0,sum1) mod n, where sum0 is the sum of previous terms with even indices, sum1 with odd indices.

1, 1, 1, 2, 3, 5, 1, 0, 8, 4, 3, 5, 4, 7, 9, 14, 4, 2, 2, 0, 19, 11, 9, 16, 17, 3, 0, 25, 8, 5, 7, 4, 5, 2, 1, 34, 29, 26, 10, 6, 8, 4, 4, 0, 41, 10, 6, 8, 4, 4, 0, 48, 34, 30, 1, 52, 43, 38, 12, 6, 6, 0, 57, 52, 34, 28, 50, 44, 13, 6, 5, 70, 61, 54, 26, 18, 28

Offset

1,4

Comments

Conjecture: every integer appears infinitely many times.

From Rémy Sigrist, Mar 30 2018: (Start)

The sequence is 2-periodic in the interval n = 669..717: in this interval, a(2*k) = 176 and a(2*k+1) = 264.

The sequence is 2-periodic in the interval n = 585469..588887: in this interval, a(2*k) = 146528 and a(2*k+1) = 219792.

The sequence is 2-periodic in the interval n = 481689629..481728001: in this interval, a(2*k) = 120425588 and a(2*k+1) = 180638382.

(End)

The sequence of indices of zeros begins: 8, 20, 27, 44, 51, 62, 319, 836, 1280, 2216, 2320, 4318, 24075, 94832, 125815, 155635, 459384, 471600, 683516, 6870325... - Alex Ratushnyak, Feb 21 2020

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 2000 terms from Rémy Sigrist)

Rémy Sigrist, Colored scatterplot of the sequence for n = 1..1000000

Rémy Sigrist, Scatterplot of the sequence for n = 550000..600000

Example

a(8) = max(5+2+1,1+3+1+1) mod 8 = 0.

Maple

s:= proc(n) s(n):= `if`(n<1, 0, a(n)+s(n-2)) end:
a:= proc(n) a(n):= `if`(n<2, n, irem(max(s(n-1), s(n-2)), n)) end:
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 31 2018

Mathematica

s[n_] := s[n] = If[n < 1, 0, a[n] + s[n-2]];
a[n_] := a[n] = If[n < 2, n, Mod[Max[s[n-1], s[n-2]], n]];
Array[a, 100] (* Jean-François Alcover, May 31 2019, from Maple *)

Prog

(Python)
a = [1]
s0 = 0
s1 = 1
for n in range(2, 1000):
    v = max(s1, s0) % n
    a.append(v)
    if n&1:  s1 += v
    else:    s0 += v
print(a)
(PARI) lista(nn) = {my(va = [], na = 1, s0 = 0, s1 = 0); print1(na, ", "); va = concat(va, na); for (n=2, nn, if (n % 2, s1 += na, s0 += na); na = max(s0, s1) % n; print1(na, ", "); va = concat(va, na); ); } \\ Michel Marcus, Mar 05 2018

Crossrefs

Cf. A332581.

Sequence in context: A171034 A062007 A031067 * A335706 A339640 A031027

Adjacent sequences: A300389 A300390 A300391 * A300393 A300394 A300395

Keyword

nonn

Author

Alex Ratushnyak, Mar 05 2018

Status

approved