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%I A309334 #18 Jul 26 2019 15:08:50
%S A309334 4,6,18,6,6,24,6,6,48,24,12,30,18,12,18,42,24,24,18,18,42,12,12,30,24,
%T A309334 54,36,24,12,6,12,12,30,54,12,30,18,36,60,54,54,6,12,12,18,48,6,24,6,
%U A309334 78,30,18,42,12,156,12,72,24,12,18,66,30,30,54,24,30,48,54
%N A309334 Lucky prime gaps: differences between consecutive lucky primes.
%C A309334 Since (except for 3) all lucky primes == 1 (mod 6), a(n) >= 6 for n >= 2. - _Robert Israel_, Jul 26 2019
%H A309334 Robert Israel, <a href="/A309334/b309334.txt">Table of n, a(n) for n = 1..10000</a>
%F A309334 a(n) = A031157(n+1) - A031157(n).
%e A309334 a(1) = 4 because difference between the first (3) and second (7) lucky prime is 4.
%e A309334 a(2) = 6 because difference between 7 and 13 is 6.
%p A309334 N:= 10^4: # for lucky primes up to 2*N+1
%p A309334 L:= [seq(2*i+1, i=0..N)]:
%p A309334 for n from 2 while n < nops(L) do
%p A309334   r:= L[n];
%p A309334   L:= subsop(seq(r*i=NULL, i=1..nops(L)/r), L);
%p A309334 od:
%p A309334 LP:= select(isprime,L):
%p A309334 LP[2..-1]-LP[1..-2]; # _Robert Israel_, Jul 26 2019
%o A309334 (SageMath)
%o A309334 [A031157[i+1]-A031157[i] for i in range(100)]
%Y A309334 Cf. A031157, A001223, A309333.
%K A309334 nonn
%O A309334 1,1
%A A309334 _Hauke Löffler_, Jul 24 2019

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