%I A113604
%S A113604 2,2,3,23,5,0,7,23,0,11,11,0,13,19,0,23,17,0,19,41,0,41,23,0,37,41,0,
%T A113604 101,29,0,31,37,0,41,43,0,37,101,0,59,41,0,43,59,0,67,47,0,101,89,0,59,
%U A113604 53,0,89,67,0,71,59,0,61,101,0,127,89,0,67,103,0,101,71,0,73,127,0,89
%N A113604 Define f(k) = k + sum of digits of n. a(n) is the first prime that results 
               by applying f zero or more times to n, or 0 if no such prime exists.
%C A113604 a(n) = n for n prime; a(n) = 0 for n > 3 and n == 0 (mod 3).
%C A113604 Conjecture: a(n) = 0 only if n == 0 (mod 3).
%e A113604 a(4) = 23 since f(4) = 4+4 = 8, f(8) = 8+8 = 16, f(16) = 16+1+6 = 23.
%o A113604 (PARI) f(n) = local(k,s,d);k=n;s=0;while(k>0,d=divrem(k,10);k=d[1];s=s+d[2]);
               s+n {m=76;for(n=1,m,if(n>3&&n%3==0,print1(0,","),k=n;z=1000*n;while(k<z&&!isprime(k),
               k=f(k));print1(if(k<z,k,0),",")))}
%Y A113604 Cf. A113605.
%Y A113604 Sequence in context: A058157 A049132 A087768 this_sequence A084745 A036503 
               A109590
%Y A113604 Adjacent sequences: A113601 A113602 A113603 this_sequence A113605 A113606 
               A113607
%K A113604 base,easy,nonn
%O A113604 1,1
%A A113604 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 09 2005
%E A113604 Edited and extended byKlaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Nov 10 2005