A343145 a(n) is the least positive number k such that applying x->prime(x) n times results in a number that ends in k.
1, 7, 6447, 7, 1, 1, 69, 9, 1, 1, 1, 7, 1, 1
Offset: 0
Examples
a(1) = 7 since prime(7) = 17 which ends in 7. a(2) = 6447 since prime(prime(6447)) = 806447 which ends in 6447. a(3) = 7 since prime(prime(prime(7)))=277 which ends in 7. a(4) = 1 since prime(prime(prime(prime(1)))) = 11 which ends in 1. a(5) = 1 since prime(prime(prime(prime(prime(1))))) = 31 which ends in 1. a(6) = 69 since prime(prime(prime(prime(prime(prime(69)))))) = 54615469 which ends in 69. a(7) = 9 since prime(prime(prime(prime(prime(prime(prime(9))))))) = 4535189 which ends in 9.
Programs
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PARI
primemap(n, tms) = my(x=n); for(i=1, tms, x=prime(x)); x enddigits(n, len) = ((n/10^len - floor(n/10^len)) * 10^len) a(n) = for(k=1, oo, my(x=k); if(enddigits(primemap(k, n), #Str(k))==k, return(k))) \\ Felix Fröhlich, Apr 14 2021
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Python
def A343145(n): k = 1 while True: m = k for _ in range(n): m = prime(m) if m % 10**(len(str(k))) == k: return k k += 1 while not (k % 2 and k % 5): k += 1