A375328 Terms as well as digits fit the prime/prime/nonprime pattern; this is the lexicographically earliest injective sequence with this property.

2, 3, 0, 5, 7, 1, 23, 13, 20, 37, 17, 21, 53, 43, 24, 73, 47, 26, 229, 239, 22, 67, 29, 25, 83, 31, 27, 97, 59, 32, 127, 137, 4, 251, 271, 33, 157, 173, 6, 331, 359, 35, 433, 457, 8, 379, 521, 52, 653, 673, 9, 571, 739, 55, 677, 823, 12, 71, 751, 57, 827, 853, 15, 79, 2203, 28, 2207, 263, 30, 2213, 283, 34, 2243

Offset

1,1

Links

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

Example

a(4) = 5, a(5) = 7, a(6) = 1, a(7) = 23, a(8) = 13, a(9) = 20; we see that a(4), a(5), a(7) and a(8) are primes and that a(6) and a(9) are nonprimes. The digits involved fit the pattern prime/prime/nonprime too; they are 5,7,1,2,3,1,3,2 and 0.

Prog

(Python)
from sympy import isprime
from itertools import count, islice, product
def bgen(i): # generates terms with p/p/np, p/np/p, or np/p/p 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, A375327.

Sequence in context: A324640 A364574 A122830 * A344137 A350260 A358276

Adjacent sequences: A375325 A375326 A375327 * A375329 A375330 A375331

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Aug 13 2024

Status

approved