A375326 Terms as well as digits fit the nonprime/prime pattern; this is the lexicographically earliest injective sequence with this property.

0, 2, 1, 3, 4, 5, 6, 7, 8, 29, 20, 31, 21, 59, 24, 71, 26, 79, 28, 263, 9, 283, 12, 13, 15, 17, 42, 43, 45, 47, 62, 67, 63, 83, 65, 97, 82, 131, 30, 293, 85, 139, 34, 307, 87, 151, 36, 313, 92, 179, 38, 317, 93, 421, 39, 347, 95, 431, 50, 367, 120, 383, 121, 397, 124, 503, 126, 547, 128, 563, 129, 587, 130

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Aug 12 2024

Keywords

• base
• nonn

Examples

			a(9) = 8, a(10) = 29, a(11) = 20, a(12) = 31; we see that a(9) and a(11) are nonprimes and that a(10) and a(12) are primes. The digits involved fit the pattern nonprime/prime too; they are 8, 2, 9, 2, 0, 3, 1.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A217555.

Programs

Python

from sympy import isprime
from itertools import count, islice, product
def bgen(i): # generates terms with prime/nonprime or nonprime/prime digits
    digs = ["014689", "2357"]
    for digits in count(1):
        patt = [digs[(i+j)&1] for j in range(digits)]
        yield from (int("".join(s)) for s in product(*patt) if s[0]!="0")
def agen(): # generator of terms
    seen, s, an = {0, 2}, 2, 2
    yield from [0, 2]
    for n in count(3):
        p = (n&1) == 0
        an = next(k for k in bgen(s) if k not in seen and isprime(k)==p)
        yield an
        seen.add(an)
        s += len(str(an))
print(list(islice(agen(), 99))) # Michael S. Branicky, Aug 12 2024