%I
%S 2,23,211,773,773,13367,3411949,236122171,3129706267,3314192745739,
%T 711114155396657,331149818444273,3331113965338635107,
%U 3331113965338635107,7241721710291471119,3318308475676071413
%N The smallest prime p for which there is an integer m such that the home sequence of m has n terms and terminates at p.
%C Starting number is: 2, 6, 4, 25, 10, 14, 45, 91, 78, 40, 150, 135, 126, 8, 104, 20, 212, 86, 87, 65, 340, 604, 894, 341, 123, 105, 345, 1810, ..., .  _Robert G. Wilson v_, Sep 22 2007
%H P. De Geest, <a href="http://www.worldofnumbers.com/topic1.htm">Home Primes < 100 and Beyond</a>
%e 23 is the home prime of both 6 and 23, thus a(2) = 23; 211 is the home prime of 6, 22 and 211, thus a(3) = 211.
%t t = Table[0, {28}]; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], { #[[2]] }] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[ a = h@n; If[ t[[Length@a]] == 0, t[[Length@a]] = a[[ 1]]; Print[{Length@a, n, a[[ 1]]}]], {n, 2, 2500}]; t (* _Robert G. Wilson v_, Sep 22 2007 *)
%Y Cf. A037274, A118756.
%K nonn,base
%O 1,1
%A William Lindgren (william.lindgren(AT)sru.edu) & _Robert G. Wilson v_, Sep 30 2007
