A065863 Remainder when n-th prime is divided by the number of nonprimes not exceeding n.

0, 0, 0, 1, 1, 1, 2, 3, 3, 5, 1, 2, 6, 3, 2, 3, 9, 6, 1, 11, 8, 9, 13, 14, 1, 16, 13, 12, 14, 13, 7, 5, 5, 1, 5, 1, 7, 7, 5, 5, 11, 7, 17, 13, 11, 7, 19, 25, 23, 19, 17, 17, 19, 23, 23, 23, 23, 19, 25, 23, 25, 29, 37, 35, 31, 29, 43, 43, 47, 43, 47, 47, 3, 2, 1, 53, 53, 55, 2, 3, 6, 1, 11, 6

Offset

1,7

Links

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

Formula

a(n) = prime(n) mod (n - pi(n)) = A000040(n) mod A062298(n).

Example

n=25, p(25)=97, n - pi(n) = 25 - 9 = 16, a(25)=1 because 97 = 6*16 + 1.

Mathematica

Table[Mod[Prime[n], n-PrimePi[n]], {n, 90}] (* Harvey P. Dale, Aug 04 2015 *)

Prog

(PARI) { for (n = 1, 1000, a=prime(n)%(n - primepi(n)); write("b065863.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 02 2009

Crossrefs

Cf. A000040, A062298, A065858-A065864, A065134, A004648, A065133, A065134.

Sequence in context: A127641 A328730 A106821 * A341931 A341701 A049272

Adjacent sequences: A065860 A065861 A065862 * A065864 A065865 A065866

Keyword

nonn

Author

Labos Elemer, Nov 26 2001

Status

approved