A389725 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) = 5.

5, 59, 859, 9859, 99859, 998759, 9987569, 99887569, 998987569, 9989875697, 99989875697, 999989875697, 9999898756973, 99998987569703, 999989875969703, 9999898765969703, 99998989765969703, 999989897659569703, 9999898977659569703, 99999898977659569703, 999998998977659569703

Offset

1,1

Comments

Starting with 8 gives 8, 89, 859, ..., matching this sequence from a(3) onward.

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 = 5, -1
    while an > prevan:
        yield an
        an, prevan = f(an), an
print(list(islice(agen(), 21)))

Crossrefs

Cf. A389720, A389721, A389722, A389723, A389724, A389726, A389727.

Sequence in context: A020468 A093946 A249519 * A371327 A001059 A385952

Adjacent sequences: A389722 A389723 A389724 * A389726 A389727 A389728

Keyword

nonn,base

Author

Michael S. Branicky, Oct 16 2025

Status

approved