A389724 a(n) is the greatest prime > a(n-1) obtained by inserting a single digit anywhere in its string of digits (including at the beginning or end), starting with a(1) = 4.

4, 47, 947, 9547, 97547, 997547, 9978547, 99785947, 997895947, 9978959747, 99798959747, 998798959747, 9989798959747, 99897989597647, 998979989597647, 9989799895979647, 99899799895979647, 998997998959796047, 9989997998959796047, 99899979989959796047, 998999979989959796047

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..1000

Prog

(Python)
from gmpy2 import is_prime
from itertools import islice
def f(n): # A389720
    s = str(n)
    return max((p for i in range(len(s)+1) for d in "0123456789" if is_prime(p:=int(s[:i]+d+s[i:]))), default=-1)
def agen(): # generator of terms
    an, prevan = 4, -1
    while an > prevan:
        yield an
        an, prevan = f(an), an
print(list(islice(agen(), 21)))

Crossrefs

Cf. A389720, A389721, A389722, A389723, A389725, A389726, A389727.

Sequence in context: A326434 A319833 A006438 * A380830 A251665 A210828

Adjacent sequences: A389721 A389722 A389723 * A389725 A389726 A389727

Keyword

nonn,base

Author

Michael S. Branicky, Oct 16 2025

Status

approved