A246805 - OEIS

%I #19 Nov 07 2022 13:46:14

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

%T 171234891469

%N 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).

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

%C Is this sequence infinite?

%H Paul Tek, <a href="/A246805/a246805.gp.txt">PARI program for this sequence</a>

%e The following concatenations are prime:

%e - j=2: a(1) U a(2)=13, a(2) U a(1)=31

%e - j=3: a(3) U a(1)=41, a(3) U a(2)=43

%e - 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

%e - 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

%e - 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

%o (PARI) See Link section.

%o (Python)

%o from sympy import isprime

%o from itertools import islice

%o def c(s, slst):

%o     return all(isprime(int(s+t)) or isprime(int(t+s)) for t in slst)

%o def agen():

%o     slst, an, mink = [], 1, 2

%o     while True:

%o         yield an; slst.append(str(an)); an += 1

%o         while not c(str(an), slst): an += 1

%o print(list(islice(agen(), 10))) # _Michael S. Branicky_, Oct 17 2022

%Y Cf. A156770, A228323.

%K base,nonn,more

%O 1,2

%A _Paul Tek_, Nov 16 2014

%E a(15) from _Michael S. Branicky_, Nov 07 2022