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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).
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%I #9 Jun 24 2023 01:25:44

%S 2,3,23,5,7,37,11,211,311,13,313,17,317,1117,19,719,1319,23,223,523,

%T 1123,1723,29,229,1129,31,331,1931,37,337,3137,41,241,541,1741,2341,

%U 43,743,47,347,547,1747,2347,53,353,1153,1753,2953,4153,59,359

%N 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 Michael S. Branicky, <a href="/A114101/b114101.txt">Table of n, a(n) for n = 1..10000</a>

%e 11 is followed by 211, 311 (511 and 711 are not primes); then 13.

%o (Python)

%o from itertools import islice

%o from sympy import isprime, nextprime

%o def agen(): # generator of terms

%o p, s = 2, []

%o while True:

%o yield p; sp = str(p); s.append(sp); p = nextprime(p)

%o yield from filter(isprime, (int("".join(si + sp)) for si in s))

%o print(list(islice(agen(), 51))) # _Michael S. Branicky_, Jun 23 2023

%Y Cf. A114007.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Nov 20 2005

%E More terms from Amy Postell (arp179(AT)psu.edu), Feb 02 2006

%E Offset changed to 1 by _Michael S. Branicky_, Jun 23 2023