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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A141583 A147413 A066137 * A147428 A147436 A189118

Adjacent sequences: A269659 A269660 A269661 * A269663 A269664 A269665

Keyword

nonn

Author

K. D. Bajpai, Mar 02 2016

Status

approved