A210712 Primes formed by concatenating n, n, n, and 1 for n = 1, 2, 3,....

2221, 3331, 4441, 6661, 1212121, 1616161, 2323231, 2424241, 2828281, 3131311, 3232321, 3333331, 3636361, 3838381, 4040401, 4242421, 4545451, 5454541, 5858581, 6262621, 6868681, 6969691, 7171711, 7272721, 8282821, 9090901, 9999991, 1161161161

Offset: 1

Author

Jonathan Vos Post, Jan 29 2013

Keywords

• nonn
• base
• easy

Comments

This is to three (duplicated strings concatenated) as A210511 is to two (duplicated strings concatenated).

Examples

			a(1) = 2221 because "2" concatenated with "2" concatenated with "2" concatenated with "1" = 2221, which is prime.
9393931 is not in the sequence, even though formed by concatenating n, n, n, and 1 for n = 93, because 9393931 = 211^3 is composite.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A210511.

Programs

Magma

[nnn1: n in [1..120] | IsPrime(nnn1) where nnn1 is Seqint([1] cat Intseq(n) cat Intseq(n) cat Intseq(n))]; // Bruno Berselli, Jan 30 2013

Mathematica

Select[Table[FromDigits[Flatten[{IntegerDigits[n], IntegerDigits[n], IntegerDigits[n], IntegerDigits[1],{}}]], {n, 1000}], PrimeQ] (* Vincenzo Librandi, Mar 13 2013 *)
Select[FromDigits/@Table[Flatten[IntegerDigits/@PadLeft[{1},4,n]],{n,120}],PrimeQ] (* Harvey P. Dale, May 12 2015 *)

PARI

a(n) = { my(p=Str(prime(n))); eval(concat(concat(concat(p,p),p),1)); } /* Joerg Arndt, Mar 14 2013 */