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

1,1

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A000040, A001358.

Sequence in context: A151796 A113580 A242124 * A242123 A229787 A329147

Adjacent sequences: A117319 A117320 A117321 * A117323 A117324 A117325

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 08 2006

Status

approved