A389727 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) = 7.

7, 97, 997, 9973, 99793, 997973, 9987973, 99987973, 999879773, 9998797073, 99987970783, 999879970783, 9999879970783, 99998799707083, 999987999707083, 9999879997097083, 99998799970970839, 999987999709707839, 9999879997097097839, 99998799997097097839, 999987999970970976839

Offset

1,1

Comments

Starting with 9 gives 9, 97, ..., matching this sequence from a(2) onward.

Starting with 0 gives 7, so it would be 0 followed by this sequence.

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 = 7, -1
    while an > prevan:
        yield an
        an, prevan = f(an), an
print(list(islice(agen(), 21)))

Crossrefs

Cf. A389720, A389721, A389722, A389723, A389724, A389725, A389726.

Sequence in context: A178007 A241206 A127892 * A125590 A068694 A158579

Adjacent sequences: A389724 A389725 A389726 * A389728 A389729 A389730

Keyword

nonn,base

Author

Michael S. Branicky, Oct 16 2025

Status

approved