A073310 a(n) is the smallest number k such that 2+k and 2n+k are both prime.

1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 5, 3, 1, 1, 5, 3, 1, 3, 1, 1, 3, 1, 5, 3, 1, 5, 3, 1, 1, 5, 3, 1, 3, 1, 1, 5, 3, 1, 3, 1, 5, 3, 1, 11, 5, 3, 1, 3, 1, 1, 3, 1, 1, 3, 1, 17, 11, 9, 11, 5, 3, 1, 3, 1, 5, 3, 1, 1, 9, 9, 5, 3, 1, 1, 5, 3, 1, 5, 3, 1, 3, 1, 5, 3, 1, 5, 3, 1, 1, 9, 9, 5, 3, 1, 1, 3, 1, 1, 11, 9, 29

Offset: 1

Author

T. D. Noe, Aug 02 2002

Keywords

• easy
• nonn

Comments

Conjecture: a(n) < 2n. See A073316 for a generalization for all positive even numbers less than 2n.

Examples

			a(45) = 11 because 11 is the smallest number yielding two primes when added to 2 and 90. This is the first instance where this sequence differs from A060266.
		

Crossrefs

Cf. A060266, A073316.

Programs

Mathematica

maxN=200; lst={}; For[n=1, n<=maxN, n++, k=1; While[k<2n&&!(PrimeQ[k+2]&&PrimeQ[k+2n]), k=k+2]; AppendTo[lst, k]; If[k>2n, Print["Failure at n = ", n]]]; lst