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Integers whose Reverse And Add trajectory reaches its first prime after a record number of iterations (at least one iteration must be performed).
0

%I #16 Jul 10 2021 00:08:50

%S 1,5,181,10031,1001320

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

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

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

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

%o (PARI) f(n) = my(t=n, c=1); while(!isprime(t+=fromdigits(Vecrev(digits(t)))), if(gcd(t, 33)>1, return(0)); c++); c;

%o lista(nn) = my(m); for(k=1, nn, if(f(k)>m, print1(k, ", "); m=f(k))); \\ _Jinyuan Wang_, Jun 15 2021

%o (Python)

%o from sympy import isprime

%o def ra(n): s = str(n); return int(s) + int(s[::-1])

%o def afind(limit):

%o record = 0

%o for k in range(limit+1):

%o m, i = ra(k), 1

%o while not isprime(m) and m%3 != 0 and m%11 != 0: m = ra(m); i += 1

%o if isprime(m) and i > record: record = i; print(k, end=", ")

%o afind(1234567) # _Michael S. Branicky_, Jul 03 2021

%Y Cf. A056964.

%K nonn,base,more

%O 1,2

%A _Daniel Starodubtsev_, Jun 14 2021