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

1,2

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A217555.

Sequence in context: A035043 A288118 A155963 * A273863 A273864 A058684

Adjacent sequences: A375320 A375321 A375322 * A375327 A375328 A375329

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Aug 12 2024

Status

approved