A065870 n-th prime - n-th semiprime.

-2, -3, -4, -3, -3, -2, -4, -3, -2, 3, -2, 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, 138, 142, 149, 154, 158, 157, 154, 160, 154, 160

Offset: 1

Author

Robert A. Stump (bee_ess107(AT)yahoo.com), Dec 07 2001

Keywords

• easy
• sign

Examples

			Prime_1 - semiprime_1 = 2 - 4 = -2, prime_2 - semiprime_2 = 3 - 6 = -3, prime_3 - semiprime_3 = 5 - 9 = -4, etc.
		

Links

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

Crossrefs

Cf. A000040, A001358, A038529 (n-th prime - n-th composite).

Programs

Mathematica

  nn=250;Module[{pr=Prime[Range[nn]],sp=Select[Range[nn],PrimeOmega[ #]==2&],len}, len=Min[nn,Length[sp]];#[[1]]-#[[2]]&/@ Thread[ {Take[ pr,len],Take[sp,len]}]](* Harvey P. Dale, Aug 14 2013 *)

PARI

m=0; for (n=4, 250, if (bigomega(n) == 2, m = m + 1; print1(prime(m) - n,",")))

PARI

n=m=0; for (k=1, 10^9, if (bigomega(k) != 2, next); m = m + 1; write("b065870.txt", n++, " ", prime(m) - k); if (n==1000, return) ) \\ Harry J. Smith, Nov 02 2009

Formula

a(n) = A000040(n) - A001358(n). - Zak Seidov, Apr 29 2015

Extensions

More terms from Rick L. Shepherd, Mar 09 2002