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A136344 Least primes p1 such that gap between p1 and p2=nextprime(p1) contains no semiprimes. Gap is 1 for n=0 (first term) and 2n for n=1..30. 0

%I #5 Apr 19 2013 10:17:32

%S 2,11,97,601,6473,2521,35117,63113,39343,104659,705053,512821,1123279,

%T 4357781,4942711,4808987,5922317,32995057,105484481,37212113,

%U 108525829,335433389,598559963,789565537,864056573,1913815493,2311939579

%N Least primes p1 such that gap between p1 and p2=nextprime(p1) contains no semiprimes. Gap is 1 for n=0 (first term) and 2n for n=1..30.

%C Indices of primes are: 1, 5, 25, 110, 840, 369, 3745, 6329, 4142, 9990, 56934, 42502, 87392, 306589, 344750, 336038, 407897, 2031387, 6058935, 2273894, 6223604, 18062361, 31253527, 40636901, 44264857, 94194169, 112738722, 128926127, 19290534, 258502581, 413356835. Notice that indices (and primes) are not necessarily monotonically increasing. Cf. A133478 (semiprime gaps without primes).

%e a(1)=2 because gap=3-2=1 and between 2 and 3 there is no semiprimes,

%e a(2)=11 because gap=11-13=2 and between 11 and 13 there is no semiprimes,

%e a(3)=97 because gap=97-101=4 and between 97 and 101 there is no semiprimes,

%e a(31)=9042022037 because gap=9042022037-9042022097=60 and between 9042022037 and 9042022097 there is no semiprimes.

%Y Cf. A133478.

%K nonn

%O 1,1

%A _Zak Seidov_, Dec 24 2007

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Last modified April 25 07:53 EDT 2024. Contains 371964 sequences. (Running on oeis4.)