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Primes formed by concatenating n with n+1 and by concatenating n+2 with n+3.
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%I #15 Nov 17 2018 17:41:57

%S 67,89,7879,8081,9091,9293,186187,188189,276277,278279,426427,428429,

%T 438439,440441,450451,452453,600601,602603,606607,608609,798799,

%U 800801,816817,818819,858859,860861,936937,938939,960961,962963,11401141,11421143

%N Primes formed by concatenating n with n+1 and by concatenating n+2 with n+3.

%C Subsequence of A030458.

%C First bisection: A156121.

%H Bui Quang Tuan, <a href="/A256176/b256176.txt">Table of n, a(n) for n = 1..100</a>

%e 67, 89 are in the sequence because they are primes and 6, 7, 8, 9 are four consecutive integers.

%e 7879, 8081 are in the sequence because they are primes and 78, 79, 80, 81 are four consecutive integers.

%e 186187, 188189 are in the sequence because they are primes and 186, 187, 188, 189 are four consecutive integers.

%t f[n_] := FromDigits@ Flatten[IntegerDigits /@ Range[n, n + 1]]; {f@ #, f[# + 2]} & /@ Select[Range@ 1200, AllTrue[{f@ #, f[# + 2]}, PrimeQ] &] // Flatten (* _Michael De Vlieger_, Mar 18 2015 *)

%t fd[{a_,b_}]:=FromDigits[Join[IntegerDigits[a],IntegerDigits[b]]]; Select[ {fd[ Take[#,2]],fd[Take[#,-2]]}&/@Partition[Range[1500],4,1],AllTrue[ #,PrimeQ]&]//Flatten (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 17 2018 *)

%o (PARI) lista(nn) = {for (n=1, nn, if (isprime(p=eval(concat(Str(n), Str(n+1)))) && isprime(q=eval(concat(Str(n+2), Str(n+3)))), print1(p, ", ", q, ", ")););} \\ _Michel Marcus_, Mar 18 2015

%K nonn,base

%O 1,1

%A _Bui Quang Tuan_, Mar 18 2015