A133796 a(n) = n-th prime + n-th semiprime.

6, 9, 14, 17, 25, 28, 38, 41, 48, 55, 64, 71, 76, 81, 86, 99, 108, 112, 122, 128, 131, 141, 148, 158, 171, 178, 185, 192, 195, 200, 218, 224, 231, 234, 255, 262, 272, 281, 286, 294, 301, 304, 320, 326, 331, 340, 353, 366, 372, 375, 388, 397, 400, 412, 423, 432

Offset: 1

Author

Jonathan Vos Post, Jan 05 2008

Keywords

• easy
• nonn

Examples

			a(1) = 1st prime + 1st semiprime = 2 + 4 = 6.
a(2) = 2nd prime + 2nd semiprime = 3 + 6 = 9.
a(3) = 3rd prime + 3rd semiprime = 5 + 9 = 14.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Crossrefs

Cf. A000040, A001358.

Programs

Maple

A000040 := proc(n) ithprime(n) ; end: A001358 := proc(n) option remember ; local a ; if n = 1 then 4 ; else for a from A001358(n-1)+1 do if numtheory[bigomega](a) = 2 then RETURN(a) ; fi ; od: fi ; end: A133796 := proc(n) A000040(n)+A001358(n) ; end: seq(A133796(n),n=1..100) ; # R. J. Mathar, Jan 07 2008

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]; f[n_] := Prime@n + SemiPrime@n; Array[f, 56] (* Robert G. Wilson v *)
Module[{nn=300,pr,semi,len},pr=Prime[Range[PrimePi[nn]]];semi=Select[ Range[ nn], PrimeOmega[#]==2&];len=Min[Length[pr],Length[semi]];Total/@ Thread[{Take[pr,len],Take[semi,len]}]] (* Harvey P. Dale, Jun 27 2014 *)

PARI

A133796(n)=prime(n)+A001358(n) \\ M. F. Hasler, Apr 24 2019

Formula

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

Extensions

Corrected and extended by Robert G. Wilson v and R. J. Mathar, Jan 05 2008

Typo in first Mma program corrected by Giovanni Resta, Jun 12 2016