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A175839 Smallest runs of n*2-1 consecutive composites.

%I A175839 #12 May 09 2021 09:39:50
%S A175839 4,8,9,10,24,25,26,27,28,90,91,92,93,94,95,96,114,115,116,117,118,119,
%T A175839 120,121,122,114,115,116,117,118,119,120,121,122,123,124,114,115,116,
%U A175839 117,118,119,120,121,122,123,124,125,126
%N A175839 Smallest runs of n*2-1 consecutive composites.
%C A175839 Even lengths of runs of composites are omitted, as nontrivial runs always have odd lengths (see A046933).
%C A175839 Run 5 (starting at 114) has 13 consecutive composites and is repeated in runs 6 and 7. Run 8 starts at 524 = A008950(6).
%H A175839 Wikipedia, <a href="http://en.wikipedia.org/wiki/Composite_number">Composite number</a>
%e A175839 Run 1 has length 1; the first composite is 4.
%e A175839 Run 2 has length 3; the first three consecutive composites are 8, 9, and 10.
%e A175839 Run 3 has length 5; the first five consecutive composites are 24, 25, 26, 27, and 28.
%e A175839 4;
%e A175839 8, 9, 10;
%e A175839 24, 25, 26, 27, 28;
%e A175839 90, 91, 92, 93, 94, 95, 96;
%e A175839 114, 115, 116, 117, 118, 119, 120, 121, 122;
%e A175839 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124;
%e A175839 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126;
%o A175839 (Python)
%o A175839 from sympy import isprime
%o A175839 out = []
%o A175839 run = 1
%o A175839 for n in range(4, 10000):
%o A175839     isrun = True
%o A175839     for o in range(run): isrun *= not isprime(n + o - run)
%o A175839     if isrun:
%o A175839         for o in range(run): out.append(n + o - run)
%o A175839         run += 2
%o A175839 print(out)
%Y A175839 Cf. A002808, A046933, A008950.
%K A175839 easy,nonn
%O A175839 1,1
%A A175839 _Grant Garcia_, Sep 20 2010