A256176 Primes formed by concatenating n with n+1 and by concatenating n+2 with n+3.

67, 89, 7879, 8081, 9091, 9293, 186187, 188189, 276277, 278279, 426427, 428429, 438439, 440441, 450451, 452453, 600601, 602603, 606607, 608609, 798799, 800801, 816817, 818819, 858859, 860861, 936937, 938939, 960961, 962963, 11401141, 11421143

Offset: 1

Author

Bui Quang Tuan, Mar 18 2015

Keywords

• nonn
• base

Comments

Subsequence of A030458.

First bisection: A156121.

Examples

			67, 89 are in the sequence because they are primes and 6, 7, 8, 9 are four consecutive integers.
7879, 8081 are in the sequence because they are primes and 78, 79, 80, 81 are four consecutive integers.
186187, 188189 are in the sequence because they are primes and 186, 187, 188, 189 are four consecutive integers.
		

Links

• Bui Quang Tuan, Table of n, a(n) for n = 1..100

Programs

Mathematica

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 *)
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 *)

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