|
%I #20 Sep 06 2017 16:04:58
%S 5711,111317,171923,313741,414347,8997101,229233239,239241251,
%T 263269271,307311313,313317331,317331337,353359367,359367373,
%U 383389397,389397401,401409419,409419421,439443449,449457461
%N Primes which are concatenations of three consecutive primes.
%C a(n) = "p(k) p(k+1) p(k+2)" where p(k) is k-th prime
%C It is conjectured that sequence is infinite. - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
%D Richard E. Crandall, Carl Pomerance: Prime Numbers, Springer 2005 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
%D John Derbyshire: Prime obsession, Joseph Henry Press, Washington, DC 2003 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
%D Marcus du Sautoy: Die Musik der Primzahlen. Auf den Spuren des groessten Raetsels der Mathematik, Beck, Muenchen 2004
%H Zak Seidov, <a href="/A030469/b030469.txt">Table of n, a(n) for n = 1..1000</a>
%F A132903 INTERSECT A000040. - _R. J. Mathar_, Nov 11 2009
%e (1) 5=p(3), 7=p(4), 11=p(5) gives a(1).
%e (2) 7=p(4), 11=p(5), 13=p(6), but 71113 = 7 x 10159
%t Select[Table[FromDigits[Flatten[IntegerDigits/@{Prime[n],Prime[n+1],Prime[n+2]}]],{n,11000}],PrimeQ] (* _Zak Seidov_, Oct 16 2009 *)
%t concat[{a_,b_,c_}]:=FromDigits[Flatten[IntegerDigits/@{a,b,c}]]; Select[ concat/@ Partition[ Prime[ Range[200]],3,1],PrimeQ] (* _Harvey P. Dale_, Sep 06 2017 *)
%o (PARI) for(i=1,999, isprime(p=eval(Str(prime(i),prime(i+1),prime(i+2)))) & print1(p," ")) \\ _M. F. Hasler_, Nov 10 2009
%Y Cf. A030461, A167517, A132903, A068655, A030997, A030473, A086041, A099727.
%K nonn,base
%O 1,1
%A _Patrick De Geest_
|
