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A086043 Concatenation of first n twin primes.

%I A086043 #30 Apr 03 2023 10:36:10
%S A086043 3,35,357,35711,3571113,357111317,35711131719,3571113171929,
%T A086043 357111317192931,35711131719293141,3571113171929314143,
%U A086043 357111317192931414359,35711131719293141435961,3571113171929314143596171,357111317192931414359617173,357111317192931414359617173101
%N A086043 Concatenation of first n twin primes.
%C A086043 After 3, 357111317192931414359 is the only prime in the sequence for n up to 10000.
%C A086043 Although 5 appears in two twin prime pairs (3, 5) and (5, 7), 5 is concatenated only once in the sequence. - _Daniel Forgues_, Aug 23 2016
%C A086043 a(n) == 0 mod 3 for n odd, a(n) == 2 mod 3 for n even. - _Robert Israel_, Sep 01 2016
%H A086043 Robert Israel, <a href="/A086043/b086043.txt">Table of n, a(n) for n = 1..270</a>
%H A086043 C. K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=TwinPrime">Twin Primes</a>.
%H A086043 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.
%p A086043 Primes:= select(isprime, {seq(i,i=1..100,2)}):
%p A086043 T1:= Primes intersect map(`+`,Primes,2):
%p A086043 Twins:= sort(convert(T1 union map(`-`,T1,2),list)):
%p A086043 dcat:= (a,b) -> a*10^(1+ilog10(b))+b:
%p A086043 A[1]:= 3:
%p A086043 for n from 2 to nops(Twins) do A[n]:= dcat(A[n-1],Twins[n]) od:
%p A086043 seq(A[i],i=1..nops(Twins)); # _Robert Israel_, Sep 01 2016
%t A086043 Table[FromDigits@ Flatten@ Map[IntegerDigits, Take[#, n]], {n, Length@ #}] &[Union@ Join[#, # + 2] &@ Select[Prime@ Range@ 17, NextPrime@ # - 2 == # &]] (* _Michael De Vlieger_, Sep 01 2016 *)
%t A086043 Module[{tps=Union[Flatten[Select[Partition[Prime[Range[50]],2,1],#[[2]]-#[[1]] == 2&]]]},FromDigits[Flatten[IntegerDigits/@#]]&/@Table[Take[tps,n],{n,Length[tps]}]] (* _Harvey P. Dale_, Jun 16 2022 *)
%o A086043 (PARI) concattwprb(n) = { y=3; forprime(x=5,n, if(isprime(x+2) || isprime(x-2), y=eval(concat(Str(y),Str(x))); print1(y",") ) ) }
%Y A086043 Cf. A001097 (twin primes), A086080, A086158.
%Y A086043 Cf. A007908, A019518, A059996, A078795, A089933, A092447.
%K A086043 easy,nonn,base
%O A086043 1,1
%A A086043 _Cino Hilliard_, Sep 08 2003
%E A086043 Edited by _N. J. A. Sloane_, Jul 01 2008 at the suggestion of _R. J. Mathar_