A246805 Lexicographically earliest sequence of distinct terms such that, when i<j, at least one of a(i) U a(j) or a(j) U a(i) is prime (where U denotes concatenation).

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

Offset

1,2

Comments

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

Is this sequence infinite?

Links

Table of n, a(n) for n=1..15.

Paul Tek, PARI program for this sequence

Example

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

Prog

(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

Crossrefs

Cf. A156770, A228323.

Sequence in context: A042227 A117789 A169892 * A241660 A338452 A030724

Adjacent sequences: A246802 A246803 A246804 * A246806 A246807 A246808

Keyword

base,nonn,more

Author

Paul Tek, Nov 16 2014

Extensions

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

Status

approved