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%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
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