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A262159 a(1) = 1, for n > 1 the least composite number k > a(n-1) such that a(n-1) + k is also a composite number.

%I A262159 #19 Oct 06 2015 08:27:13
%S A262159 1,8,10,12,14,16,18,20,22,24,25,26,28,30,32,33,35,39,42,44,46,48,50,
%T A262159 52,54,56,58,60,62,63,65,68,70,72,74,76,77,78,80,81,84,85,86,88,90,92,
%U A262159 93,94,95,99,102,104,105,108,110,111,114,116,118,119,121,122,123,124,125,128,130,132,133,134
%N A262159 a(1) = 1, for n > 1 the least composite number k > a(n-1) such that a(n-1) + k is also a composite number.
%C A262159 For n > 2, a(n) - a(n-1) <= 4.
%H A262159 Peter Kagey, <a href="/A262159/b262159.txt">Table of n, a(n) for n = 1..10000</a>
%e A262159 The first composite number is 4, but 1 + 4 = 5, which is prime, and also 1 + 6 = 7 also prime. Since 1 + 8 = 9 = 3^2, a(2) = 8.
%e A262159 After 8, 9 is also composite but 8 + 9 = 17, which is prime. But 10 works: 8 + 10 = 18 = 2 * 3^2, hence a(3) = 10.
%p A262159 m:= 0:
%p A262159 for n from 1 to 100 do
%p A262159   for k from m+1 while isprime(k) or isprime(m+k) do od:
%p A262159   a[n]:= k;
%p A262159   m:= k;
%p A262159 od:
%p A262159 seq(a[i],i=1..100); # _Robert Israel_, Sep 20 2015
%t A262159 a = {1}; Do[k = a[[n - 1]] + 1; While[Nand[CompositeQ@ k, CompositeQ[a[[n - 1]] + k]], k++]; AppendTo[a, k], {n, 2, 72}]; a (* _Michael De Vlieger_, Sep 17 2015 *)
%o A262159 (PARI) lista(nn) = {print1(a = 1, ", "); for(n=1, nn, forcomposite(k=a+1,, if (!isprime(a+k), print1(k, ", "); a = k; break);););} \\ _Michel Marcus_, Sep 20 2015
%Y A262159 Cf. A072525 (similar but with prime sums).
%K A262159 nonn
%O A262159 1,2
%A A262159 _Gionata Neri_, Sep 13 2015
%E A262159 a(51)-a(70) from _Michael De Vlieger_, Sep 17 2015