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A114101 Begin with prime(1), then prime(2). After prime(j) write all the primes of the form prime(i) concatenated with prime(j) with i then prime(j+1).

%I A114101 #9 Jun 24 2023 01:25:44
%S A114101 2,3,23,5,7,37,11,211,311,13,313,17,317,1117,19,719,1319,23,223,523,
%T A114101 1123,1723,29,229,1129,31,331,1931,37,337,3137,41,241,541,1741,2341,
%U A114101 43,743,47,347,547,1747,2347,53,353,1153,1753,2953,4153,59,359
%N A114101 Begin with prime(1), then prime(2). After prime(j) write all the primes of the form prime(i) concatenated with prime(j) with i<j; then prime(j+1).
%H A114101 Michael S. Branicky, <a href="/A114101/b114101.txt">Table of n, a(n) for n = 1..10000</a>
%e A114101 11 is followed by 211, 311 (511 and 711 are not primes); then 13.
%o A114101 (Python)
%o A114101 from itertools import islice
%o A114101 from sympy import isprime, nextprime
%o A114101 def agen(): # generator of terms
%o A114101     p, s = 2, []
%o A114101     while True:
%o A114101         yield p; sp = str(p); s.append(sp); p = nextprime(p)
%o A114101         yield from filter(isprime,  (int("".join(si + sp)) for si in s))
%o A114101 print(list(islice(agen(), 51))) # _Michael S. Branicky_, Jun 23 2023
%Y A114101 Cf. A114007.
%K A114101 base,nonn
%O A114101 1,1
%A A114101 _Amarnath Murthy_, Nov 20 2005
%E A114101 More terms from Amy Postell (arp179(AT)psu.edu), Feb 02 2006
%E A114101 Offset changed to 1 by _Michael S. Branicky_, Jun 23 2023