A065862 Remainder when n-th composite number is divided by the number of nonprimes not exceeding n.

0, 0, 0, 1, 0, 0, 2, 3, 1, 0, 2, 0, 1, 0, 7, 6, 7, 6, 8, 8, 7, 6, 7, 6, 6, 5, 4, 4, 6, 5, 6, 6, 5, 4, 3, 2, 4, 3, 2, 1, 2, 2, 4, 3, 2, 1, 2, 2, 1, 0, 0, 0, 1, 0, 38, 38, 39, 39, 40, 41, 42, 42, 42, 42, 43, 43, 44, 44, 44, 44, 45, 46, 47, 47, 48, 49, 49, 49, 51, 52, 52, 52, 54, 54, 54, 54, 54

Offset: 1

Author

Labos Elemer, Nov 26 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002808, A000720, A062298, A065858-A065864, A065134.

Programs

Mathematica

Module[{nn=150,cmps,len},cmps=Select[Range[nn],CompositeQ];len=Length[ cmps];Mod[#[[1]],#[[2]]-PrimePi[#[[2]]]]&/@Thread[{cmps,Range[len]}]] (* Harvey P. Dale, Feb 21 2020 *)

PARI

Composite(n) = { local(k); k=n + primepi(n) + 1; while (k != n + primepi(k) + 1, k = n + primepi(k) + 1); return(k) } { for (n = 1, 1000, a=Composite(n)%(n - primepi(n)); write("b065862.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 02 2009

Formula

a(n) = c(n) mod (n - pi(n)) = A002808(n) mod (n - A000720(n)) = A002808(n) mod A062298(n).