A137625
The initial prime in the first set of n consecutive primes for which p+4 is semiprime.
Original entry on oeis.org
2, 29, 173, 709, 1741, 8297, 8297, 19213, 175229, 175229, 33952609, 4377722623, 4377722623, 1242030992173, 1242030992173
Offset: 1
a(2)=29 because this is the first prime in a run of 2 consecutive primes -- 29 and 31 -- where p+4 is semiprime, i.e., 29+4 and 31+4 are both semiprimes.
A137626
The largest prime in the first set of n consecutive primes for which p+4 is semiprime.
Original entry on oeis.org
2, 31, 181, 733, 1777, 8363, 8369, 19273, 175333, 175349, 33952819, 4377722977, 4377723013, 1242030992717, 1242030992723
Offset: 1
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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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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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
A137628
Semiprimes (p+4) associated with last prime in A137626.
Original entry on oeis.org
6, 35, 185, 737, 1781, 8367, 8373, 19277, 175337, 175353, 33952823, 4377722981, 4377723017, 1242030992721, 1242030992727
Offset: 1
a(2)=35 because when p=29 (resp. 31), p+4=33 (resp. 35) and are semiprime (3*3 resp. 5*7).
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