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

1,2

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A072525 (similar but with prime sums).

Sequence in context: A220571 A033872 A080752 * A020744 A356657 A008557

Adjacent sequences: A262156 A262157 A262158 * A262160 A262161 A262162

Keyword

nonn

Author

Gionata Neri, Sep 13 2015

Extensions

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

Status

approved