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

1,4

Comments

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

Links

Table of n, a(n) for n=1..102.

Example

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.

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

Crossrefs

Cf. A060266, A073316.

Sequence in context: A281680 A377864 A060266 * A174414 A046929 A377776

Adjacent sequences: A073307 A073308 A073309 * A073311 A073312 A073313

Keyword

easy,nonn

Author

T. D. Noe, Aug 02 2002

Status

approved