A073367 Remainder when n-th composite is divided by number of composites not exceeding n.

0, 0, 0, 0, 0, 0, 3, 0, 3, 4, 3, 1, 8, 0, 8, 0, 10, 9, 8, 9, 8, 8, 7, 6, 6, 8, 7, 8, 8, 7, 6, 5, 4, 6, 5, 4, 3, 4, 4, 6, 5, 4, 3, 4, 4, 3, 2, 2, 2, 3, 2, 1, 0, 0, 40, 0, 0, 1, 0, 43, 43, 44, 44, 45, 45, 45, 45, 46, 47, 48, 48, 49, 50, 50, 50, 52, 53, 53, 53, 55, 55, 55, 55, 55, 55, 56, 56, 56

Offset

4,7

Links

Michael De Vlieger, Table of n, a(n) for n = 4..10000

Formula

a(n) = A002808(n) mod A065855(n).

Example

For n=4: a(4) = composite(4) mod (4-Pi(4)-1) = 9 mod 1 = 0; n=19:
a(19) = composite(19) mod (19-Pi(19)-1) = 30 mod 10 = 0.

Mathematica

f[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] Table[Mod[f[w], w-PrimePi[w]-1], {w, 1, 128}]

Crossrefs

Cf. A002808, A065855.

Sequence in context: A210877 A127753 A197736 * A222769 A111862 A277092

Adjacent sequences: A073364 A073365 A073366 * A073368 A073369 A073370

Keyword

nonn

Author

Labos Elemer, Jul 30 2002

Extensions

Edited by Michael De Vlieger, Nov 05 2020

Status

approved