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A375328
Terms as well as digits fit the prime/prime/nonprime pattern; this is the lexicographically earliest injective sequence with this property.
2
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
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
KEYWORD
base,nonn
AUTHOR
STATUS
approved