cp's OEIS Frontend

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

%I A117322 #14 Nov 21 2021 19:00:38
%S A117322 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,
%T A117322 21,22,23,26,36,38,43,44,43,40,42,45,48,52,57,58,62,60,63,58,69,80,82,
%U A117322 83,78,81,82,90,91,94,92,93,94,96,96,99,106,109,110,112,125,128,134,135
%N A117322 a(n) = prime(n) modulo semiprime(n).
%H A117322 Harvey P. Dale, <a href="/A117322/b117322.txt">Table of n, a(n) for n = 1..1000</a>
%F A117322 a(n) = A000040(n) modulo A001358(n).
%e A117322 a(1) = 2 mod 4 = 2.
%e A117322 a(2) = 3 mod 6 = 3.
%e A117322 a(3) = 5 mod 9 = 5.
%e A117322 a(4) = 7 mod 10 = 7.
%e A117322 a(5) = 11 mod 14 = 11.
%t A117322 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 *)
%t A117322 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 *)
%Y A117322 Cf. A000040, A001358.
%K A117322 easy,nonn
%O A117322 1,1
%A A117322 _Jonathan Vos Post_, Mar 08 2006