A127417 a(1)=1; for n > 1, a(n) = number of earlier terms a(k), 1 <= k <= n-1, such that (a(k)+n) is divisible by k.

1, 1, 2, 2, 2, 2, 3, 2, 2, 4, 3, 1, 4, 3, 2, 5, 2, 4, 4, 1, 2, 6, 4, 1, 6, 3, 3, 5, 2, 4, 3, 4, 3, 6, 4, 2, 3, 5, 5, 4, 3, 3, 7, 2, 2, 7, 4, 3, 5, 3, 4, 5, 6, 3, 3, 4, 2, 6, 6, 4, 6, 4, 5, 3, 3, 5, 5, 3, 3, 7, 6, 2, 6, 5, 4, 5, 2, 5, 8, 1, 5, 6, 5, 1, 6, 7, 3, 9, 2, 4, 5, 2, 5, 6, 6, 5, 5, 4, 4, 6, 4, 4, 6, 3, 4

Offset

1,3

Comments

The value of a(1) = 1 is arbitrary. a(1) can be any integer and the rest of the sequence would remain unchanged.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(1)+11 = 12 is a multiple of 1; a(2)+11 = 12 is a multiple of 2; and a(7)+11 = 14 is a multiple of 7. These 3 are the only cases where (a(k)+11) is a multiple of k, for 1 <= k <= 10. So a(11) = 3.

Maple

N:= 200: # to get a(1)..a(N)
A[1]:= 1:
for n from 2 to N do
  A[n]:= nops(select(t -> ((A[t]+n)/t)::integer, [$1..n-1]))
od:
seq(A[i], i=1..N); # Robert Israel, Aug 17 2018

Mathematica

f[l_List] := Block[{n = Length[l] + 1}, Append[l, Count[Table[Mod[l[[k]] + n, k], {k, n - 1}], 0]]]; Nest[f, {1}, 105] (* Ray Chandler, Jan 22 2007 *)

Crossrefs

Cf. A127418.

Sequence in context: A322861 A237259 A235614 * A308622 A198897 A201375

Adjacent sequences: A127414 A127415 A127416 * A127418 A127419 A127420

Keyword

nonn

Author

Leroy Quet, Jan 13 2007

Extensions

Extended by Ray Chandler, Jan 22 2007

Status

approved