A063378 Smallest number whose Sophie Germain degree (see A063377) is n.

4, 7, 3, 11, 5, 2, 89, 1122659, 19099919, 85864769, 26089808579, 665043081119, 554688278429, 4090932431513069, 95405042230542329

Offset: 0

Author

Reiner Martin, Jul 14 2001

Keywords

• hard
• more
• nonn

Comments

Also known as Cunningham chains of length n of the first kind.

For each positive integer n, is there some integer with Sophie Germain degree of n?

Examples

			Using f(x)=2x+1, 11 -> 23 -> 47 -> 95, which is composite; thus a(3)=11.
		

Links

• Warut Roonguthai, Yves Gallot's Proth.exe and Cunningham Chains

Crossrefs

Cf. A005384, A063377.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; f[n_] := Block[{k = 2}, While[ Length[ NestWhileList[2# + 1 &, k, PrimeQ]] != n + 1, k = NextPrim[k]]; k]; Table[f[n], {n, 1, 8}]

Extensions

More terms from Jud McCranie, Jul 20 2001

Edited and extended by Robert G. Wilson v, Nov 21 2002