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Least prime such that between it and the next prime there are exactly n semiprimes.
2

%I #15 Aug 17 2013 17:25:15

%S 2,3,7,31,89,139,113,211,1381,1637,1129,2557,2971,1327,15683,16141,

%T 9973,35677,34061,43331,19609,107377,162143,44293,404597,461717,

%U 838249,155921,535399,492113,396733,2181737,370261,1468277,6034247,3933599,1671781,25180171

%N Least prime such that between it and the next prime there are exactly n semiprimes.

%C a(62) = 1294268491, a(64) = 2300942549.

%H Giovanni Resta, <a href="/A228171/b228171.txt">Table of n, a(n) for n = 0..91</a>

%F a(n) is the prime precessing A228170(n-1).

%e a(2) = 7 since between 7 and the next prime, 11, there are 2 semiprimes (9, 10).

%t t = Table[0, {100}]; p=3; While[p < 3100000000, q = NextPrime[p]; a = Count[ PrimeOmega[ Range[p, q]], 2]; If[ t[[a]] == 0, t[[a]] = p; Print[{p, a}]]; p = q]; t

%Y Cf. A133478, A228170.

%K nonn

%O 0,1

%A _Jack Brennen_, _Jonathan Vos Post_, _Zak Seidov_, and _Robert G. Wilson v_, Aug 14 2013