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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A008557 A161425

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

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Last modified August 8 21:27 EDT 2022. Contains 356016 sequences. (Running on oeis4.)