A392041 Smallest prime number whose decimal digits include the consecutive pattern 1, 2, ..., n.

11, 127, 1123, 12343, 123457, 12345623, 71234567, 1234567801, 1234567891, 1234567891003, 12345678910111, 12345678910111207, 912345678910111213, 123456789101112131449, 12345678910111213141523, 123456789101112131415161, 41234567891011121314151617, 31234567891011121314151617181

Offset

1,1

Comments

a(369) has 1002 digits. - Michael S. Branicky, Dec 29 2025

Links

Michael S. Branicky, Table of n, a(n) for n = 1..368

Formula

A007908(n) <= a(n) <= A053546(n). - Michael S. Branicky, Dec 29 2025

Prog

(Python)
from gmpy2 import is_prime, mpz
from itertools import count, product
def a(n):
    s = "".join(str(i) for i in range(1, n+1))
    t = mpz(s)
    if is_prime(t): return int(t)
    cands = set()
    for d in count(1):
        for w in product("0123456789", repeat=d):
            w = "".join(w)
            for i in range(d+1):
                v = w[:i] + s + w[i:]
                if v[0] != "0" and is_prime(t:=mpz(v)):
                    cands.add(t)
        if cands:
            return int(min(cands))
print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Dec 29 2025

Crossrefs

Cf. A007908, A053546, A058183, A176942.

Sequence in context: A048394 A088628 A069599 * A053546 A084975 A065543

Adjacent sequences: A392038 A392039 A392040 * A392042 A392043 A392044

Keyword

nonn,base

Author

Jean-Marc Rebert, Dec 29 2025

Status

approved