cp's OEIS Frontend

A106582 Numbers which are the concatenation of two primes.

%I A106582 #22 May 28 2025 12:39:03
%S A106582 22,23,25,27,32,33,35,37,52,53,55,57,72,73,75,77,112,113,115,117,132,
%T A106582 133,135,137,172,173,175,177,192,193,195,197,211,213,217,219,223,229,
%U A106582 231,232,233,235,237,241,243,247,253,259,261,267,271,273,279,283,289
%N A106582 Numbers which are the concatenation of two primes.
%C A106582 A105184 and A121609 are subsequences.
%H A106582 T. D. Noe, <a href="/A106582/b106582.txt">Table of n, a(n) for n = 1..10000</a>
%H A106582 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/23198.html">Prime Curios! 17257</a>
%e A106582 133 is in the sequence because 133 = 13*10+3 = A000040(6)*10+A000040(2).
%t A106582 nn=500; t=Union[Reap[Do[n=FromDigits[Join[IntegerDigits[Prime[i]], IntegerDigits[Prime[j]]]]; If[n<=nn, Sow[n]], {i,PrimePi[nn/10]}, {j,PrimePi[nn/IntegerDigits[nn][[1]]]}]][[2,1]]] (* _T. D. Noe_, Mar 11 2011 *)
%t A106582 Take[FromDigits[Flatten[IntegerDigits/@#]]&/@Tuples[Prime[Range[30]],2]//Union,60] (* _Harvey P. Dale_, May 28 2025 *)
%o A106582 (Python)
%o A106582 from sympy import isprime
%o A106582 from itertools import count, islice
%o A106582 def agen(): # generator of terms
%o A106582     for k in count(1):
%o A106582         s = str(k)
%o A106582         if any(s[i] != '0' and isprime(int(s[:i])) and isprime(int(s[i:])) for i in range(1, len(s))):
%o A106582             yield k
%o A106582 print(list(islice(agen(), 55))) # _Michael S. Branicky_, Feb 26 2022
%Y A106582 Cf. A001358, A105184, A121609.
%K A106582 base,nonn
%O A106582 1,1
%A A106582 _Eric Angelini_ and _Robert G. Wilson v_, May 09 2005
%E A106582 Corrected by _Arkadiusz Wesolowski_, Mar 11 2011