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.

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

Offset: 1

Author

Amarnath Murthy, Nov 09 2005

Keywords

• base
• easy
• nonn

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).

Examples

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

Crossrefs

Cf. A113605.

Programs

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
				

Extensions

Edited and extended by Klaus Brockhaus, Nov 10 2005