%I #6 May 13 2013 00:52:42

%S 2,29,23,347,293,239,57487,486193,1725121513,1221261395831,

%T 28549657193411

%N a(n) begins the earliest chain of exactly n distinct primes such that any term in the chain equals the previous term increased by the product of its digits.

%C A chain ends either at a composite number, or at a prime which contains a zero, since the subsequent primes in the chain are identical.

%e 23 starts the earliest chain of length 3, since 23+2*3 = 29, 29+2*9 = 47 and 47+4*7 = 75, where the first 3 terms are distinct and prime, so a(3) = 23. The last distinct term in the chain starting at 1725121513 is the prime 1725980623 which contains a zero and thus generates itself.

%t seq = 0*Range[8]; p = 2; While[p < 500000, v = Length@ NestWhileList[# + Times @@ IntegerDigits@# &, p, PrimeQ@#2 && #1 != #2 &, 2] - 1; If[ seq[[v]] == 0, seq[[v]] = p]; p = NextPrime@p]; seq

%Y Cf. A090009, A145280.

%K nonn,base

%O 1,1

%A _Giovanni Resta_, May 10 2013