A390019 Smallest prime number != n obtained by removing or adding a single digit anywhere in n, or 0 if no such prime exists.

2, 11, 23, 13, 41, 53, 61, 17, 83, 19, 101, 101, 2, 3, 149, 5, 163, 7, 181, 109, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 401, 241, 2, 3, 443, 5, 461, 7, 487, 149, 5, 5, 2, 3, 5, 5, 5, 5, 5, 5, 601, 461, 2, 3, 641, 5, 661, 7, 683, 269, 7, 7, 2, 3, 7, 5

Offset

0,1

Comments

Digits can be prepended or appended. Any leading 0 digits upon prepending or removal of the first digit are discarded.

The condition a(n) != n is the same as disallowing prepending by zero in A389929. First differs from A389929 at a(2) = 23 != 2 = A389929(2).

a(9387527) = 0 is the first prime p with a(p) = 0.

Links

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

Formula

a(p) > p or 0 for p in A125001.

Example

a(2) = 23 since deletiing and prepending cannot produce a prime and 21 and 22 are composite.

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 not (i==0 and d=='0') and is_prime(p:=int(s[:i]+d+s[i:])))
    return min(A, default=0)
print([a(n) for n in range(76)])

Crossrefs

Cf. A389929.

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

Sequence in context: A018351 A004642 A346497 * A185545 A001032 A045386

Adjacent sequences: A390016 A390017 A390018 * A390020 A390021 A390022

Keyword

nonn,base

Author

Michael S. Branicky, Oct 22 2025

Status

approved