Comment from Hans Havermann, Nov 06 2005: Fibonacci is the next (probable) prime whose integer digits sum to a prime. Thus the next term would be 21925 digits long.
Table of n, a(n) for n=1..8.
514229 is a prime fibonacci number and the sum of the digits 5+1+4+2+2+9 = 23 is also a prime.
Cf. A065398, A051694, A051694, A067515.
Sequence in context: A259378 A155011 A065406 * A205668 A118505 A067799
Adjacent sequences: A111328 A111329 A111330 * A111332 A111333 A111334
Stefan Steinerberger, Nov 05 2005