A375327 Terms as well as digits fit the nonprime/nonprime/prime pattern; this is the lexicographically earliest injective sequence with this property.

0, 1, 2, 4, 6, 3, 8, 9, 5, 10, 20, 13, 14, 21, 17, 16, 24, 43, 18, 26, 47, 40, 28, 67, 44, 30, 83, 46, 34, 97, 48, 36, 131, 12, 49, 7, 60, 38, 139, 15, 64, 29, 42, 66, 31, 45, 68, 59, 62, 69, 71, 63, 80, 79, 65, 81, 211, 39, 82, 11, 50, 85, 19, 51, 87, 41, 54, 92, 61, 56, 93, 89, 58, 95, 103, 84, 70, 151, 120

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Aug 13 2024

Keywords

• base
• nonn

Examples

			a(9) = 5, a(10) = 10, a(11) = 20, a(12) = 13, a(13) = 14, a(14) = 21 ; we see that a(9) and a(12) are primes and that a(10), a(11), a(13); and a(14) are nonprimes. The digits involved fit the pattern nonprime/nonprime/prime too; they are 5,1,0,2,0,1,3,1,4,2 and 1.
		

Links

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

Crossrefs

Cf. A217555, A375326, A375328.

Programs

Python

from sympy import isprime
from itertools import count, islice, product
def bgen(i): # generates terms with np/np/p, np/p/np, or p/np/np digits
    digs = ["014689", "2357"]
    for digits in count(1):
        patt = [digs[(i+j)%3 == 2] for j in range(digits)]
        yield from (int("".join(s)) for s in product(*patt) if digits==1 or s[0]!="0")
def agen(): # generator of terms
    seen, s = set(), 0
    for n in count(1):
        p = (n-1)%3 == 2
        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 13 2024