A389723 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) = 3.

3, 83, 983, 9883, 98893, 988963, 9889673, 98896793, 988986793, 9889867913, 98898867913, 988988677913, 9889886779193, 98899886779193, 988999886779193, 9898999886779193, 98989998986779193, 998989998986779193, 9989899989986779193, 99898999989986779193, 998989999989986779193

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 = 3, -1
    while an > prevan:
        yield an
        an, prevan = f(an), an
print(list(islice(agen(), 21)))

Crossrefs

Cf. A389720, A389721, A389722, A389724, A389725, A389726, A389727.

Sequence in context: A173811 A093166 A379603 * A111648 A013518 A166241

Adjacent sequences: A389720 A389721 A389722 * A389724 A389725 A389726

Keyword

nonn,base

Author

Michael S. Branicky, Oct 16 2025

Status

approved