A155874 Smallest positive composite number such that a(n)+n is also composite.

4, 8, 4, 6, 4, 4, 4, 8, 4, 6, 4, 4, 4, 8, 4, 6, 4, 4, 4, 6, 4, 4, 4, 4, 4, 8, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 8, 4, 6, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 8, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 8, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 4, 8, 4, 6, 4

Offset: 0

Author

Eric Angelini, Jan 29 2009

Keywords

• easy
• nonn

Comments

a(0)=4. Adding a(0) to n=0 gives 4+0=4, which is a composite number; adding a(1) to n=1 gives 8+1=9 which is composite; adding a(2) to n=2 gives 4+2=6 which is composite; adding a(3) to n=3 gives 6+3=9 which is composite; etc.

At least one of {n+4, n+6, n+8} is divisible by 3, so a(n) is in {4,6,8} for all n. - Charlie Neder, Dec 28 2018

Links

• Charlie Neder, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A122984.

Programs

PARI

a(n) = {forcomposite(k=4, 10, if (!isprime(k+n), return(k)););} \\ Michel Marcus, Dec 28 2018

Formula

If n+4 is in A001359, a(n) = 8. If n+4 is in A067774, a(n) = 6. Otherwise, a(n) = 4. - Charlie Neder, Dec 28 2018

Extensions

More terms from Charlie Neder, Dec 28 2018