A284214 Remainder when sum of first n terms of A006949 is divided by n.

0, 0, 0, 1, 2, 3, 5, 0, 2, 4, 6, 9, 0, 3, 7, 12, 0, 4, 8, 12, 17, 1, 6, 12, 19, 0, 6, 13, 21, 29, 7, 16, 25, 0, 8, 16, 24, 33, 4, 13, 23, 34, 2, 12, 23, 35, 0, 12, 25, 38, 0, 12, 25, 39, 53, 12, 27, 42, 57, 13, 29, 45, 62, 16, 33, 50, 0, 16, 32, 48, 65, 11, 28, 46, 65, 8, 26, 45, 65, 5

Offset: 1

Author

Altug Alkan, Mar 23 2017

Keywords

• nonn

Comments

Sequence represents e(n, 1) where e(n, i) = (Sum_{k=0..n-1} A006949(k)) mod (n*i).

See also alternative scatterplot and graph of this sequence in Links section.

Examples

			a(6) = 3 because Sum_{k=0..5} A006949(k) = 1 + 1 + 1 + 2 + 2 + 2 = 9 and remainder when 9 is divided by 6 is 3.
		

Links

• Altug Alkan, Table of n, a(n) for n = 1..20000
• Altug Alkan, Alternative graph of A284214
• Altug Alkan, Alternative scatterplot of A284214
• Altug Alkan, Illustration of residue classes modulo 4

Crossrefs

Cf. A006949, A282891, A283025.

Programs

Mathematica

a[0] = a[1] = a[2] = 1; a[n_] := a[n] = a[n - 1 - a[n - 1]] + a[n - 2 - a[n - 2]]; MapIndexed[Mod[#1, First@ #2] &, Accumulate@ Table[a@ n, {n, 0, 79}]] (* Michael De Vlieger, Mar 24 2017 *)

Formula

a(n) = (Sum_{k=0..n-1} A006949(k)) mod n.