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%I #10 Jan 01 2016 13:32:22
%S 11,11,7,3,7,5,13,13,7,3,5,7,5,3,3,7,3,3,3,3,11,5,5,7,3,5,3,3,3,23,3,
%T 3,5,11,7,3,5,11,23,7,3,7,3,13,11,3,3,5,3,5,11,5,3,19,3,5,3,5,7,3,13,
%U 3,13,23,11,3,5,3,11,23,3,5,3,3,13,3,11,3,5,7,7,5,5,17,5,3,11,3,3,3,23,11,7
%N Smallest odd prime q such that pq+2 is semiprime, where p is the n-th odd prime.
%C This is the second row of the infinite array: A(k,n) = Smallest odd prime q such that pq+k is semiprime, where p is the n-th odd prime. The odd semiprimes arising begin: 35, 57, 51, 35, 57, 93, 87, 249, 301, 205. The above A(k,n) = Smallest odd prime q such that pq+k is semiprime, where p is the n-th odd prime, is the 2nd plane of the infinite 3-D array: A(j,k,n) = Smallest odd prime q such that pq+k has exactly j prime factors, where p is the n-th odd prime.
%H Harvey P. Dale, <a href="/A126610/b126610.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Min {q in A065091: q*A000040(n)+2 is in A001358}.
%e a(1) = 11 because oddprime(1)*1+2 = 3*11+2 = 35 = 5*7.
%e a(2) = 11 because oddprime(2)*11+2 = 5*11+2 = 57 = 3*19.
%e a(3) = 7 because oddprime(3)*7+2 = 7*7+2 = 51 = 3*17.
%e a(4) = 3 because oddprime(4)*3+2 = 11*3+2 = 35 = 5*7.
%e a(5) = 5 because oddprime(5)*11+2 = 11*5+2 = 57 = 3*19.
%e a(6) = 7 because oddprime(6)*7+2 = 13*7+2 = 93 = 3*31.
%e a(7) = 5 because oddprime(7)*5+2 = 17*5+2 = 87 = 3*29.
%e a(8) = 13 because oddprime(8)*13+2 = 19*13+2 = 249 = 3*29.
%e a(9) = 13 because oddprime(9)*13+2 = 23*13+2 = 301 = 7*43.
%e a(10) = 7 because oddprime(10)*7+2 = 29*5+2 = 205 = 5*41.
%p isA001358 := proc(n) if numtheory[bigomega](n) = 2 then true ; else false ; fi ; end; A126610 := proc(n) local p,q ; p := ithprime(n+1) ; q := 3 ; while not isA001358(p*q+2) do q := nextprime(q) ; od ; RETURN(q) ; end ; for n from 1 to 100 do printf("%d, ",A126610(n)) ; od : # _R. J. Mathar_, Feb 10 2007
%t nn=100;sop[n_]:=Module[{prs=Prime[Range[2,nn+2]],k=1},While[ PrimeOmega[ prs[[n]] prs[[k]]+2]!=2,k++];prs[[k]]]; Array[sop,nn] (* _Harvey P. Dale_, Jan 01 2016 *)
%Y Cf. A000040, A001358, A065091, A126608-126609.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Feb 07 2007
%E More terms from _R. J. Mathar_, Feb 10 2007
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