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A375326
Terms as well as digits fit the nonprime/prime pattern; this is the lexicographically earliest injective sequence with this property.
3
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
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
KEYWORD
base,nonn
AUTHOR
STATUS
approved