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A019549 Primes formed by concatenating other primes.

%I A019549 #21 Apr 28 2025 12:20:41
%S A019549 23,37,53,73,113,137,173,193,197,211,223,227,229,233,241,257,271,277,
%T A019549 283,293,311,313,317,331,337,347,353,359,367,373,379,383,389,397,433,
%U A019549 523,541,547,557,571,577,593,613,617,673,677,719,727,733,743,757,761,773,797,977
%N A019549 Primes formed by concatenating other primes.
%H A019549 M. F. Hasler, <a href="/A019549/b019549.txt">Table of n, a(n) for n = 1..17495</a>
%H A019549 Sylvester Smith, <a href="https://www.gallup.unm.edu/~smarandache/SYLSMITH.HTM">A Set of Conjectures on Smarandache Sequences</a>, Bulletin of Pure and Applied Sciences, (Bombay, India), Vol. 15 E (No. 1), 1996, pp. 101-107.
%e A019549 113 is member as 11 and 3 are primes.
%e A019549 a(12)=227 = "2"+"2"+"7" is the first term not in A105184 (restricted to concatenation of two primes). [_M. F. Hasler_, Oct 15 2009]
%o A019549 (PARI) is_A019549(n, recurse=0)={ isprime(n) == recurse & return(recurse); for(i=1, #Str(n)-1, isprime( n%10^i ) & is_A019549( n\10^i, 1) & n\10^(i-1)%10 & return(1)) } \\ _M. F. Hasler_, Oct 15 2009
%o A019549 (Python)
%o A019549 from sympy import isprime
%o A019549 def c(n, m):
%o A019549     if m > 0 and isprime(n): return True
%o A019549     s = str(n)
%o A019549     return any(s[i]!="0" and isprime(int(s[:i])) and c(int(s[i:]), m+1) for i in range(1, len(s)))
%o A019549 def ok(n): return isprime(n) and c(n, 0)
%o A019549 print([k for k in range(978) if ok(k)]) # _Michael S. Branicky_, Sep 01 2024
%Y A019549 Cf. A105184, A152242.
%K A019549 nonn,base
%O A019549 1,1
%A A019549 R. Muller