

A126610


Smallest odd prime q such that pq+2 is semiprime, where p is the nth odd prime.


2



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, 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, 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
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OFFSET

1,1


COMMENTS

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 nth 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 nth odd prime, is the 2nd plane of the infinite 3D array: A(j,k,n) = Smallest odd prime q such that pq+k has exactly j prime factors, where p is the nth odd prime.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = Min {q in A065091: q*A000040(n)+2 is in A001358}.


EXAMPLE

a(1) = 11 because oddprime(1)*1+2 = 3*11+2 = 35 = 5*7.
a(2) = 11 because oddprime(2)*11+2 = 5*11+2 = 57 = 3*19.
a(3) = 7 because oddprime(3)*7+2 = 7*7+2 = 51 = 3*17.
a(4) = 3 because oddprime(4)*3+2 = 11*3+2 = 35 = 5*7.
a(5) = 5 because oddprime(5)*11+2 = 11*5+2 = 57 = 3*19.
a(6) = 7 because oddprime(6)*7+2 = 13*7+2 = 93 = 3*31.
a(7) = 5 because oddprime(7)*5+2 = 17*5+2 = 87 = 3*29.
a(8) = 13 because oddprime(8)*13+2 = 19*13+2 = 249 = 3*29.
a(9) = 13 because oddprime(9)*13+2 = 23*13+2 = 301 = 7*43.
a(10) = 7 because oddprime(10)*7+2 = 29*5+2 = 205 = 5*41.


MAPLE

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


MATHEMATICA

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 *)


CROSSREFS

Cf. A000040, A001358, A065091, A126608126609.
Sequence in context: A220295 A300289 A321108 * A087380 A152986 A252838
Adjacent sequences: A126607 A126608 A126609 * A126611 A126612 A126613


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Feb 07 2007


EXTENSIONS

More terms from R. J. Mathar, Feb 10 2007


STATUS

approved



