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

Author

Labos Elemer, Jul 30 2002

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A002808, A065855.

Programs

Mathematica

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

Formula

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

Extensions

Edited by Michael De Vlieger, Nov 05 2020