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

1,1

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

Table of n, a(n) for n=1..76.

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

Cf. A113605.

Sequence in context: A184846 A323609 A087768 * A084745 A192434 A189254

Adjacent sequences: A113601 A113602 A113603 * A113605 A113606 A113607

Keyword

base,easy,nonn

Author

Amarnath Murthy, Nov 09 2005

Extensions

Edited and extended by Klaus Brockhaus, Nov 10 2005

Status

approved