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

1,7

Links

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

Formula

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

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 *)

Prog

(PARI) Composite(n) = { my(k=n + primepi(n) + 1); while (k != n + primepi(k) + 1, k = n + primepi(k) + 1); return(k) }
a(n) = { Composite(n)%(n - primepi(n)) } \\ Harry J. Smith, Nov 02 2009

Crossrefs

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

Sequence in context: A031269 A006703 A133623 * A368495 A189117 A365196

Adjacent sequences: A065859 A065860 A065861 * A065863 A065864 A065865

Keyword

nonn

Author

Labos Elemer, Nov 26 2001

Status

approved