A246805 Lexicographically earliest sequence of distinct terms such that, when i

1, 3, 4, 7, 19, 31, 67, 391, 583, 4549, 917467, 6777061, 86794921, 1421517037, 171234891469

Offset: 1

Author

Paul Tek, Nov 16 2014

Keywords

• base
• nonn
• more

Comments

Two distinct terms can always be concatenated in some way to form a prime number.

Is this sequence infinite?

Examples

			The following concatenations are prime:
- j=2: a(1) U a(2)=13, a(2) U a(1)=31
- j=3: a(3) U a(1)=41, a(3) U a(2)=43
- j=4: a(1) U a(4)=17, a(4) U a(1)=71, a(2) U a(4)=37, a(4) U a(2)=73, a(3) U a(4)=47
- j=5: a(5) U a(1)=191, a(5) U a(2)=193, a(3) U a(5)=419, a(4) U a(5)=719, a(5) U a(4)=197
- j=6: a(1) U a(6)=131, a(6) U a(1)=311, a(2) U a(6)=331, a(6) U a(2)=313, a(3) U a(6)=431, a(6) U a(4)=317, a(5) U a(6)=1931, a(6) U a(5)=3119
		

Links

• Paul Tek, PARI program for this sequence

Crossrefs

Cf. A156770, A228323.

Programs

PARI

See Link section.

Python

from sympy import isprime
from itertools import islice
def c(s, slst):
    return all(isprime(int(s+t)) or isprime(int(t+s)) for t in slst)
def agen():
    slst, an, mink = [], 1, 2
    while True:
        yield an; slst.append(str(an)); an += 1
        while not c(str(an), slst): an += 1
print(list(islice(agen(), 10))) # Michael S. Branicky, Oct 17 2022

Extensions

a(15) from Michael S. Branicky, Nov 07 2022