A389929 Smallest prime number obtained by removing or adding a single digit anywhere in n, or 0 if no such prime exists.

2, 11, 2, 3, 41, 5, 61, 7, 83, 19, 101, 11, 2, 3, 149, 5, 163, 7, 181, 19, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 401, 41, 2, 3, 443, 5, 461, 7, 487, 149, 5, 5, 2, 3, 5, 5, 5, 5, 5, 5, 601, 61, 2, 3, 641, 5, 661, 7, 683, 269, 7, 7, 2, 3, 7, 5

Offset

0,1

Comments

Digits can be prepended or appended. We allow prepending by zero and any leading 0 digits upon prepending or removal of the first digit are discarded.

Links

Michael S. Branicky, Table of n, a(n) for n = 0..10000

Formula

0 < a(p) <= p for p prime.

A211396(n) <= a(n) <= A062584(n).

a(n) = 0 if n in A014263 intersection A032352.

Example

a(8) = 83 since removing any digit or prepending a digit cannot yield a prime; 80, 81 and 82 are not prime; but 83 is prime.
a(84) = 0 is the first 0 term. No removal or addition other than at the end can lead to a prime; and 841, 843, 847 and 849 are not prime.

Prog

(Python)
from gmpy2 import is_prime
def a(n):
    s = str(n)
    D = set(p for i in range(len(s)) if len(t:=s[:i]+s[i+1:]) and is_prime(p:=int(t)))
    if D: return min(D)
    A = set(p for i in range(len(s)+1) for d in "0123456789" if is_prime(p:=int(s[:i]+d+s[i:])))
    return min(A, default=0)
print([a(n) for n in range(76)])

Crossrefs

Cf. A014263, A062584, A032352, A211396, A389720, A389824, A390019.

Sequence in context: A298444 A224480 A037299 * A329941 A347121 A341512

Adjacent sequences: A389926 A389927 A389928 * A389930 A389931 A389932

Keyword

nonn,base

Author

Michael S. Branicky, Oct 19 2025

Status

approved