A126610 Smallest odd prime q such that pq+2 is semiprime, where p is the n-th odd prime.

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

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 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.

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, A126608-126609.

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