

A137626


The largest prime in the first set of n consecutive primes for which p+4 is semiprime.


3



2, 31, 181, 733, 1777, 8363, 8369, 19273, 175333, 175349, 33952819, 4377722977, 4377723013, 1242030992717, 1242030992723
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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.


LINKS

Table of n, a(n) for n=1..15.


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

Cf. A001358, A137625, A137627, A137628.
Subsequence of A289250.
Sequence in context: A229014 A042059 A343830 * A134179 A223145 A188225
Adjacent sequences: A137623 A137624 A137625 * A137627 A137628 A137629


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



