OFFSET
1,1
COMMENTS
a(n) = last prime in the first run of n primes such that p+4 is semiprime for each prime p in the run. - Sean A. Irvine, Feb 13 2012
a(n) > 5 * 10^9 for n > 13.
EXAMPLE
a(2)=31 is the largest in a set of 2 consecutive primes {29,31}, and 29 + 4 = 33 = 3*11 and 31 + 4 = 35 = 5*7 are both semiprime. No smaller number has this property.
59 is not in the sequence because although 47 + 4 = 51 = 3*17 and 53 + 4 = 57 = 3*19 are both semiprime, 59 + 4 = 63 = 3*3*7 is not.
MATHEMATICA
With[{prs=Table[If[PrimeOmega[n+4]==2, 1, 0], {n, Prime[Range[21*10^5]]}]}, Prime[ #]&/@Flatten[Table[SequencePosition[prs, PadRight[{}, n, 1], 1], {n, 11}], 1]][[All, 2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 10 2018 *)
PROG
(PARI) a(n) = {my(t = 0); forprime(p = 2, oo, if(bigomega(p + 4) == 2, t++; if(t==n, return(p)), t = 0))} \\ David A. Corneth, May 10 2018
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Enoch Haga, Jan 30 2008
EXTENSIONS
a(11) from Sean A. Irvine, Feb 12 2012
a(1) corrected by Harvey P. Dale, May 10 2018
a(12)-a(13) from David A. Corneth, May 10 2018
a(14)-a(15) from Giovanni Resta, Jun 22 2018
STATUS
approved