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A137626
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The largest prime in the first set of n consecutive primes for which p+4 is semiprime.
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3
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2, 31, 181, 733, 1777, 8363, 8369, 19273, 175333, 175349, 33952819, 4377722977, 4377723013, 1242030992717, 1242030992723
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..15.
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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more,nonn
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AUTHOR
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Enoch Haga, Jan 30 2008
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EXTENSIONS
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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
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STATUS
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approved
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