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A108605 Semiprimes with prime sum of factors: twice the lesser of the twin prime pairs. 13

%I

%S 6,10,22,34,58,82,118,142,202,214,274,298,358,382,394,454,478,538,562,

%T 622,694,838,862,922,1042,1138,1198,1234,1282,1318,1618,1642,1654,

%U 1714,1762,2038,2062,2098,2122,2182,2302,2458,2554,2578,2602,2638,2854,2902

%N Semiprimes with prime sum of factors: twice the lesser of the twin prime pairs.

%C All terms are even. (Cf. formula.)

%C The definition implies that the sum of factors is the sum over the prime factors with multiplicity, as in A001414. - _R. J. Mathar_, Nov 28 2008

%C The sum of factors of a semiprime pq is p+q, which can only be prime if {p, q} = {2, odd prime}. Requiring the sum to be prime then implies that the semiprime is twice the lesser of a twin prime pair. - _M. F. Hasler_, Apr 07 2015

%C Subsequence of A288814, each term being of the form A288814(p), where p is the greatest of a pair of twin primes. - _David James Sycamore_, Aug 29 2017

%H Charles R Greathouse IV, <a href="/A108605/b108605.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n)=2*p, with p and 2+p twin primes: a(n)=2*A001359(n).

%e 58=2*29 and 2+29 is prime.

%t Select[Range[2, 3000, 2], !IntegerQ[Sqrt[ # ]]&&Plus@@(Transpose[FactorInteger[ # ]])[[2]]==2&&PrimeQ[Plus@@(Transpose[FactorInteger[ # ]])[[1]]]&]

%o (PARI) list(lim)=my(v=List(),p=2); forprime(q=3,lim\2+1, if(q-p==2, listput(v,2*p)); p=q); Vec(v) \\ _Charles R Greathouse IV_, Feb 05 2017

%Y Cf. A001358 semiprimes, A001359 lesser of twin primes, A101605 3-almost primes, A108606 semiprimes with prime sum of digits, A108607 intersection of A108605 and A108606.

%K easy,nonn

%O 1,1

%A _Zak Seidov_, Jun 12 2005

%E Changed division by 2 to multiplication by 2 in formula related to A001359. - _R. J. Mathar_, Nov 28 2008

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Last modified September 20 08:13 EDT 2019. Contains 327214 sequences. (Running on oeis4.)