A063502 a(n+1) = p, where p is the a(n)-th twin prime (p,p+2), with a(0) = 1.

1, 3, 11, 137, 5639, 641129, 152921807, 65818751039, 46091763604421

Offset: 0

Author

Lubomir Alexandrov, Jul 30 2001

Keywords

• hard
• more
• nice
• nonn

Comments

Instead of starting with a(0) = 1 for the first twin prime (3,5) other sequences can be formed for a(0) = 2, i.e. 2nd twin prime: 2, 5, 29, 641, 44381, 7212059, etc., a(0) = 4: 4, 17, 239, 12161, 1583927, etc., a(0) = 6: 6, 41, 1151, 93251, 16989317, etc., a(0) = 7: 7, 59 1931,176021, 35263691, etc., a(0) = 8: 8, 71, 2339,221201, 45749309 and so on.

Examples

			a(3) = 137 because a(2) = 11 and the 11th twin prime is (137,139).
		

Links

• Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x) [From _M. F. Hasler_, Mar 02 2009]

Crossrefs

Cf. A007097.

Programs

Mathematica

(* Computes up to a(6) only *) tp[n_] := (* = A001359 *) tp[n] = (p = NextPrime[tp[n-1]]; While[ !PrimeQ[p+2], p = NextPrime[p]]; p); tp[1] = 3; Do[tp[n], {n, 2, 10^6}]; a[n_] := a[n] = tp[a[n-1]]; a[0]=1; Table[ Print[ a[n]]; a[n], {n, 0, 6}] (* Jean-François Alcover, Dec 13 2011 *)

Formula

a(n+1) = A001359(a(n)); a(0)=1. [M. F. Hasler, Mar 02 2009]

Extensions

Edited by Frank Ellermann, Jan 25 2002

Offset and example corrected by Farideh Firoozbakht, Dec 07 2008

a(7) = 65818751039 from Zak Seidov and Farideh Firoozbakht, Dec 13 2008

Computed a(8)=46091763604421 using data from T. Oliveira e Silva. - M. F. Hasler, Mar 02 2009