A345338 Integers whose Reverse And Add trajectory reaches its first prime after a record number of iterations (at least one iteration must be performed).

1, 5, 181, 10031, 1001320

Offset

1,2

Comments

a(6) > 10^9 (if it exists).

All numbers whose trajectory reaches a multiple of 3 or 11 before reaching a prime will never reach a prime.

Links

Table of n, a(n) for n=1..5.

Example

a(3) = 181 because it takes 3 iterations (181 -> 362 -> 625 -> 1151 (prime)) to reach a prime, which is more than any smaller number.

Prog

(PARI) f(n) = my(t=n, c=1); while(!isprime(t+=fromdigits(Vecrev(digits(t)))), if(gcd(t, 33)>1, return(0)); c++); c;
lista(nn) = my(m); for(k=1, nn, if(f(k)>m, print1(k, ", "); m=f(k))); \\ Jinyuan Wang, Jun 15 2021
(Python)
from sympy import isprime
def ra(n): s = str(n); return int(s) + int(s[::-1])
def afind(limit):
    record = 0
    for k in range(limit+1):
        m, i = ra(k), 1
        while not isprime(m) and m%3 != 0 and m%11 != 0: m = ra(m); i += 1
        if isprime(m) and i > record: record = i; print(k, end=", ")
afind(1234567) # Michael S. Branicky, Jul 03 2021

Crossrefs

Cf. A056964.

Sequence in context: A027572 A050239 A218690 * A256286 A304277 A208403

Adjacent sequences: A345335 A345336 A345337 * A345339 A345340 A345341

Keyword

nonn,base,more

Author

Daniel Starodubtsev, Jun 14 2021

Status

approved