A077068 Semiprimes of the form prime + 1.

4, 6, 14, 38, 62, 74, 158, 194, 278, 314, 398, 422, 458, 542, 614, 662, 674, 734, 758, 878, 998, 1094, 1154, 1202, 1214, 1238, 1322, 1382, 1454, 1622, 1658, 1754, 1874, 1934, 1994, 2018, 2138, 2342, 2474, 2558, 2594, 2798, 2858, 2918, 3062, 3218, 3254

Offset

1,1

Comments

a(n) = A005383(n)+1 = 2*A005382(n).

There are 672 semiprimes of form prime+1 below 100000.

a(n) = A232342(n) + A077065(n). - Reinhard Zumkeller, Dec 16 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

A010051(A008864(n)/2) = A064911(A008864(n)) = 1. - Reinhard Zumkeller, Nov 22 2013

Example

A001358(25)=74=2*37 is a term as 74=A000040(21)+1=73+1.

Mathematica

Select[Range[6000], Plus@@Last/@FactorInteger[#]==2&&PrimeQ[#-1]&] (* Vladimir Joseph Stephan Orlovsky, May 08 2011 *)
Select[ Prime@ Range@ 460 +1, PrimeOmega@# == 2 &] (* Robert G. Wilson v, Feb 18 2014 *)

Prog

(Haskell)
a077068 n = a077068_list !! (n-1)
a077068_list = filter ((== 1) . a010051 . (`div` 2)) a008864_list
-- Reinhard Zumkeller, Nov 22 2013
(PARI) [x+1|x<-primes(10^5), bigomega(x+1)==2] \\ Charles R Greathouse IV, Nov 22 2013
(PARI) is(n)=isprime(n-1) && isprime(n\2) \\ Charles R Greathouse IV, Mar 20 2016

Crossrefs

Cf. A008864, A001358, A000040, A077065, A077067.

Sequence in context: A108516 A219774 A274208 * A277059 A096003 A114058

Adjacent sequences: A077065 A077066 A077067 * A077069 A077070 A077071

Keyword

nonn

Author

Reinhard Zumkeller, Oct 23 2002

Status

approved