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.

1, 8, 10, 12, 14, 16, 18, 20, 22, 24, 25, 26, 28, 30, 32, 33, 35, 39, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 63, 65, 68, 70, 72, 74, 76, 77, 78, 80, 81, 84, 85, 86, 88, 90, 92, 93, 94, 95, 99, 102, 104, 105, 108, 110, 111, 114, 116, 118, 119, 121, 122, 123, 124, 125, 128, 130, 132, 133, 134

Offset: 1

Author

Gionata Neri, Sep 13 2015

Keywords

• nonn

Comments

For n > 2, a(n) - a(n-1) <= 4.

Examples

			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.
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.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A072525 (similar but with prime sums).

Programs

Maple

m:= 0:
for n from 1 to 100 do
  for k from m+1 while isprime(k) or isprime(m+k) do od:
  a[n]:= k;
  m:= k;
od:
seq(a[i],i=1..100); # Robert Israel, Sep 20 2015

Mathematica

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 *)

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

Extensions

a(51)-a(70) from Michael De Vlieger, Sep 17 2015