A222962 Primes of the form kk*k+k+1, where kk is the concatenation of k with itself.

13, 47, 103, 181, 281, 547, 10111, 14557, 22741, 25873, 29207, 44563, 48907, 53453, 90931, 103457, 110023, 116791, 161641, 169823, 178207, 186793, 195581, 232753, 242551, 273157, 283763, 305581, 316793, 440023, 523657, 538303, 568201, 614563, 662743

Offset: 1

Author

Vincenzo Librandi, Mar 18 2013

Keywords

• nonn
• base
• easy

Comments

Corresponding values of k are: 1, 2, 3, 4, 5, 7, 10, 12, 15, 16, 17, 21, 22, 23, 30, 32, 33, 34, 40, 41, 42, 43, 44, 48, 49, 52, 53, 55, 56, 66, 72, 73, 75, 78, 81, 82, 83, 92,...

a(7), a(43) and a(204) (see b-file) have the form 10^(3n+1)+10^(2n)+10^n+1 = (10^(n+1)*10^n+10^n)*10^n+10^n+1. The next term of this type is 10^247+10^164+10^82+1.

Examples

			22741 is in the sequence because it is prime and 22741=1515*15+15+1.
		

Links

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

Crossrefs

Cf. A020338, A157711.

Programs

Magma

[p: n in [0..100] | IsPrime(p) where p is Seqint(Intseq(n) cat Intseq(n))*n+n+1]; // Bruno Berselli, Mar 21 2013

Mathematica

f[n_] := FromDigits@Flatten@IntegerDigits[{n, n}] n + n + 1; Select[Table[f[n], {n, 100}], PrimeQ] (* Bruno Berselli, Mar 21 2013 *)
Select[Table[n(n*10^IntegerLength[n]+n)+n+1,{n,100}],PrimeQ] (* Harvey P. Dale, Oct 29 2023 *)

Extensions

Edited by Bruno Berselli, Mar 22 2013