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A175220 The fifth nonprimes after the primes.

%I A175220 #6 Jul 05 2016 19:12:35
%S A175220 10,10,12,14,18,20,24,25,28,35,36,44,48,49,52,58,65,66,74,77,78,85,88,
%T A175220 94,104,108,110,114,115,118,133,136,143,144,155,156,162,169,172,178,
%U A175220 185,186,198,200,203,204,216,230,234,235,238,245,246,256,262,268,275
%N A175220 The fifth nonprimes after the primes.
%C A175220 From _Robert Israel_, Jul 05 2016: (Start)
%C A175220 For n>1, there are the following cases:
%C A175220 If prime(n)+2 and prime(n)+4 are composite, then a(n) = prime(n)+5.
%C A175220 If exactly one of prime(n)+2 and prime(n)+4 is prime, and prime(n)+6 is composite, then a(n) = prime(n) + 6.
%C A175220 Otherwise, a(n) = prime(n) + 7. (End)
%H A175220 Robert Israel, <a href="/A175220/b175220.txt">Table of n, a(n) for n = 1..10000</a>
%p A175220 N:= 1000: # to get all entries <= N
%p A175220 Primes:= select(isprime, [2,seq(i,i=3..N+7,2)]):
%p A175220 nprimes:= nops(Primes):
%p A175220 A[1]:= 10:
%p A175220 A[2]:= 10:
%p A175220 for i from 3 to nprimes-1 do
%p A175220   p:= Primes[i];
%p A175220   if p + 5 > N then break fi;
%p A175220   if Primes[i+1] > p + 4 then A[i]:= p + 5
%p A175220   elif (i = nprimes-1 or Primes[i+2] <> p+6) and p+6 <= N  then A[i]:= p + 6
%p A175220   elif p+7 <= N then A[i]:= p + 7
%p A175220   else break
%p A175220   fi
%p A175220 od:
%p A175220 seq(A[j],j=1..i-1); # _Robert Israel_, Jul 05 2016
%K A175220 nonn
%O A175220 1,1
%A A175220 _Jaroslav Krizek_, Mar 06 2010