A389726 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) = 6.

6, 67, 967, 9967, 99767, 997637, 9978637, 99786937, 997896937, 9978969367, 99978969367, 999789693677, 9997896993677, 99978969936767, 999878969936767, 9998789969936767, 99987989969936767, 999879899699936767, 9999879899699936767, 99998798996999367677, 999987989969993676077

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 = 6, -1
    while an > prevan:
        yield an
        an, prevan = f(an), an
print(list(islice(agen(), 21)))

Crossrefs

Cf. A389720, A389721, A389722, A389723, A389724, A389725, A389727.

Sequence in context: A355051 A231598 A073562 * A354320 A230342 A239301

Adjacent sequences: A389723 A389724 A389725 * A389727 A389728 A389729

Keyword

nonn,base

Author

Michael S. Branicky, Oct 16 2025

Status

approved