A117322 a(n) = prime(n) modulo semiprime(n).

2, 3, 5, 7, 11, 13, 17, 19, 23, 3, 31, 3, 6, 5, 8, 7, 10, 10, 12, 14, 15, 17, 18, 20, 23, 24, 21, 22, 23, 26, 36, 38, 43, 44, 43, 40, 42, 45, 48, 52, 57, 58, 62, 60, 63, 58, 69, 80, 82, 83, 78, 81, 82, 90, 91, 94, 92, 93, 94, 96, 96, 99, 106, 109, 110, 112, 125, 128, 134, 135

Offset: 1

Author

Jonathan Vos Post, Mar 08 2006

Keywords

• easy
• nonn

Examples

			a(1) = 2 mod 4 = 2.
a(2) = 3 mod 6 = 3.
a(3) = 5 mod 9 = 5.
a(4) = 7 mod 10 = 7.
a(5) = 11 mod 14 = 11.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A001358.

Programs

Mathematica

SemiPrimePi[n_] := Sum[PrimePi[n/Prime@i] - i + 1, {i, PrimePi@Sqrt@n}]; SemiPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[SemiPrimePi[a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Table[ Mod[Prime@n, SemiPrime@n], {n, 70}] (* Robert G. Wilson v, May 01 2006 *)
Module[{nn=300,sprs},sprs=Select[Range[nn],PrimeOmega[#]==2&];Mod[ #[[1]],#[[2]]]&/@Thread[{Prime[Range[Length[sprs]]],sprs}]] (* Harvey P. Dale, Nov 21 2021 *)

Formula

a(n) = A000040(n) modulo A001358(n).