A261198 Start with n and repeat the map x -> x+sumdigits(x) until reaching a prime, which is a(n), or 0 if no prime is reached.

2, 23, 0, 23, 11, 0, 19, 23, 0, 11, 13, 0, 17, 19, 0, 23, 37, 0, 29, 41, 0, 41, 101, 0, 37, 41, 0, 101, 59, 0, 43, 37, 0, 41, 43, 0, 47, 101, 0, 59, 67, 0, 89, 59, 0, 67, 71, 0, 101, 89, 0, 59, 61, 0, 89, 67, 0, 71, 73, 0, 103, 101, 0, 127, 89, 0, 109, 103, 0, 101, 79, 0, 83, 127, 0, 89, 101, 0, 109, 109, 0, 103, 107, 0, 127, 101, 0, 109, 113, 0, 101, 103, 0, 107, 109, 0, 113, 127, 0, 101

Offset: 1

Author

Maghraoui Abdelkader, Sep 30 2015

Keywords

• nonn
• base

Comments

Multiples of 3 never reach a prime because (3*x + sumdigits(3*x)) is always a multiple of 3.

Examples

			a(3)=0; a(6)=0; a(9)=0  as 3,6,9 are multiples of 3.
n=2; a0=2; a1=2+sumdigits(2)=4; a2=4+sumdigits(4)=8; a3=8+sumdigits(8)=16;
a4=16+sumdigits(16)=16+7=23; a4 is prime, so a(2)=23;
a(14)=14+(1+4=19); 19 is prime.
a(16)=16+(1+6)=23; 23 is prime.
		

Links

• Maghraoui Abdelkader, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000040, A001651, A008585, A154561.

Programs

PARI

verif(n)={if((n%3)==0, print1(0,", ");return(););
b=1; a=n;
while(b<10, a=a+sumdigits(a) ;if(isprime(a),print1(a,", "); b=20))}
for(n=1, 100, verif(n);)