A077068 - OEIS

%I #32 Jan 01 2022 21:39:41

%S 4,6,14,38,62,74,158,194,278,314,398,422,458,542,614,662,674,734,758,

%T 878,998,1094,1154,1202,1214,1238,1322,1382,1454,1622,1658,1754,1874,

%U 1934,1994,2018,2138,2342,2474,2558,2594,2798,2858,2918,3062,3218,3254

%N Semiprimes of the form prime + 1.

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

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

%C a(n) = A232342(n) + A077065(n). - _Reinhard Zumkeller_, Dec 16 2013

%H Reinhard Zumkeller, <a href="/A077068/b077068.txt">Table of n, a(n) for n = 1..10000</a>

%F A010051(A008864(n)/2) = A064911(A008864(n)) = 1. - _Reinhard Zumkeller_, Nov 22 2013

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

%t Select[Range[6000],Plus@@Last/@FactorInteger[#]==2&&PrimeQ[#-1]&] (* _Vladimir Joseph Stephan Orlovsky_, May 08 2011 *)

%t Select[ Prime@ Range@ 460 +1,PrimeOmega@# == 2 &] (* _Robert G. Wilson v_, Feb 18 2014 *)

%o (Haskell)

%o a077068 n = a077068_list !! (n-1)

%o a077068_list = filter ((== 1) . a010051 . (`div` 2)) a008864_list

%o -- _Reinhard Zumkeller_, Nov 22 2013

%o (PARI) [x+1|x<-primes(10^5),bigomega(x+1)==2] \\ _Charles R Greathouse IV_, Nov 22 2013

%o (PARI) is(n)=isprime(n-1) && isprime(n\2) \\ _Charles R Greathouse IV_, Mar 20 2016

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

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Oct 23 2002