A392246 Smallest prime number whose decimal digits include the consecutive pattern 0, 1, 2, ..., n.

101, 101, 20123, 20123, 3012343, 10123457, 201234563, 401234567, 50123456783, 100123456789, 101234567891071, 1012345678910119, 101234567891011123, 1012345678910111213, 10123456789101112131421, 101234567891011121314157, 100123456789101112131415163, 1012345678910111213141516171

Offset

0,1

Comments

a(368) has 1001 digits. - Michael S. Branicky, Jan 04 2026

Links

Michael S. Branicky, Table of n, a(n) for n = 0..367

Prog

(Python)
from gmpy2 import is_prime, mpz
from itertools import count, product
def a(n):
    s = "".join(str(i) for i in range(n+1))
    cands = set()
    for d in count(1):
        for f in "123456789":
            for w in product("0123456789", repeat=d-1):
                w = "".join(w)
                for i in range(d):
                    v = f + w[:i] + s + w[i:]
                    if is_prime(t:=mpz(v)):
                        cands.add(t)
        if cands:
            return int(min(cands))
print([a(n) for n in range(19)]) # Michael S. Branicky, Jan 04 2026

Crossrefs

Cf. A007908, A053546, A058183, A176942, A392041.

Sequence in context: A283044 A284138 A284180 * A138719 A043639 A152054

Adjacent sequences: A392243 A392244 A392245 * A392247 A392248 A392249

Keyword

nonn,base

Author

Jean-Marc Rebert, Jan 04 2026

Status

approved