A269662 Semiprimes which are the sum of a twin prime pair plus one.

9, 25, 85, 121, 145, 205, 217, 301, 361, 481, 565, 697, 841, 865, 1141, 1285, 1717, 1765, 2041, 2101, 2305, 2461, 2581, 2605, 2641, 2965, 2977, 3241, 3337, 3397, 3865, 3901, 3997, 4285, 4537, 4681, 4765, 5317, 5377, 5461, 5941, 6001, 6241, 6505, 6937, 7081, 7117

Offset: 1

Author

K. D. Bajpai, Mar 02 2016

Keywords

• nonn

Comments

All the terms, except a(1), are congruent to 1 (mod 3).

Examples

			a(2) = 25 = 5 * 5 that is semiprime. Also, 25 = 11 + 13 + 1 where {11, 13} is a twin prime pair.
a(3) = 85 = 5 * 17 that is semiprime. Also, 55 = 41 + 43 + 1 where {41, 43} is a twin prime pair.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001097, A001358, A001359, A006512, A054735, A118071.

Programs

Magma

IsP2:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ s: n in [1..1000] | IsPrime(n) and IsPrime(n+2) and IsP2(s) where s is (n + n+2 + 1)];

Mathematica

A269662 = {}; Do[a = Prime[n]; b = a + 2; c = a + b + 1; If[PrimeQ[b] && PrimeOmega[c] == 2, AppendTo[A269662, c]], {n, 1000}]; A269662
Select[Range[1, 7200, 2], And[PrimeOmega@ # == 2, And[PrimeQ@ #, NextPrime[#] - 2] == # &[(# - 1)/2 - 1]] &] (* Michael De Vlieger, Apr 01 2016 *)
Select[1+Total[#]&/@Select[Partition[Prime[Range[500]],2,1],#[[2]]-#[[1]] == 2&],PrimeOmega[#]==2&] (* Harvey P. Dale, Apr 10 2016 *)

PARI

for(n = 1, 1000, p=prime(n); q=p+2; s=p+q+1; if(isprime(q) && bigomega(s)==2, print1(s,", ")));