A389722 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) = 2.

2, 29, 929, 9929, 99929, 999529, 9995329, 99975329, 999975329, 9999795329, 99997950329, 999979590329, 9999879590329, 99998795970329, 999987959760329, 9999879597860329, 99998795978603729, 999987959786037029, 9999879659786037029, 99998979659786037029, 999989799659786037029

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 = 2, -1
    while an > prevan:
        yield an
        an, prevan = f(an), an
print(list(islice(agen(), 21)))

Crossrefs

Cf. A389720, A389721, A389723, A389724, A389725, A389726, A389727.

Sequence in context: A090251 A087281 A380724 * A024234 A367551 A077282

Adjacent sequences: A389719 A389720 A389721 * A389723 A389724 A389725

Keyword

nonn,base

Author

Michael S. Branicky, Oct 16 2025

Status

approved