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

1,1

Comments

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

Links

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

Example

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.

Prog

(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); )

Crossrefs

Cf. A000040, A001651, A008585, A154561.

Sequence in context: A060601 A053952 A343263 * A052077 A124604 A374376

Adjacent sequences: A261195 A261196 A261197 * A261199 A261200 A261201

Keyword

nonn,base

Author

Maghraoui Abdelkader, Sep 30 2015

Status

approved