

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.


0



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, 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, 53, 0, 89, 67, 0, 71, 59, 0, 61, 101, 0, 127, 89, 0, 67, 103, 0, 101, 71, 0, 73, 127, 0, 89
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

a(n) = n for n prime; a(n) = 0 for n > 3 and n == 0 (mod 3).
Conjecture: a(n) = 0 only if n == 0 (mod 3).


LINKS



EXAMPLE

a(4) = 23 since f(4) = 4+4 = 8, f(8) = 8+8 = 16, f(16) = 16+1+6 = 23.


PROG

(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), ", ")))}


CROSSREFS



KEYWORD

base,easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



