A284173 a(n) = (Sum_{k=1..n} q(k+1-q(k))) mod n where q(k) = A005185(k).

0, 0, 0, 0, 1, 2, 3, 5, 7, 9, 1, 2, 4, 7, 9, 12, 15, 0, 3, 6, 9, 12, 17, 20, 0, 4, 8, 12, 16, 22, 26, 31, 4, 9, 14, 20, 26, 31, 37, 3, 8, 14, 20, 26, 32, 38, 1, 4, 11, 18, 23, 30, 39, 46, 53, 6, 12, 20, 28, 36, 44, 56, 1, 9, 21, 28, 36, 46, 57, 68, 9, 20, 30, 39, 48, 60, 69, 2, 12

Offset: 1

Author

Altug Alkan, Mar 21 2017

Keywords

• nonn

Comments

Sequence represents d(n, 1, 1) where d(n, i, j) = (Sum_{k=1..n} q(k+j-q(k))) mod (n*i) where q(k) = A005185(k).

Links

• Altug Alkan, Table of n, a(n) for n = 1..10000
• Robert Israel, Illustration Of Residue Classes Modulo 8

Crossrefs

Cf. A005185, A280706, A283025, A283467, A283509.

Programs

Maple

N:= 1000: # to get a(1) to a(N)
B[1]:= 1:
B[2]:= 1:
for n from 3 to N do
  B[n]:= B[n-B[n-1]] + B[n-B[n-2]];
od:
seq(add(B[k+1-B[k]], k=1..n) mod n, n=1..N); # Robert Israel, Mar 22 2017

Mathematica

q[n_]:=If[n<3, 1, q[n - q[n - 1]] + q[n - q[n - 2]]]; a[n_]:=Mod[Sum[q[k + 1 - q[k]],{k, n}], n]; Table[a[n], {n, 100}] (* Indranil Ghosh, Mar 21 2017 *)

PARI

a=vector(1000); a[1]=a[2]=1; for(n=3, #a, a[n]=a[n-a[n-1]]+a[n-a[n-2]]); vector(#a, n, sum(k=1, n, a[k+1-a[k]]) % n)

Scheme

(define (A284173 n) (modulo (A280706 n) n)) ;; Other code as in A280706, A283467 and A005185 - Antti Karttunen, Mar 22 2017

Formula

a(n) = A280706(n) mod n. - Antti Karttunen, Mar 22 2017