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

1,3

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A217555, A375326, A375328.

Sequence in context: A210771 A359535 A115316 * A089088 A251622 A073899

Adjacent sequences: A375320 A375321 A375326 * A375328 A375329 A375330

Keyword

base,nonn,new

Author

Eric Angelini and Jean-Marc Falcoz, Aug 13 2024

Status

approved