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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A020338, A157711.

Sequence in context: A001662 A031390 A113943 * A004467 A261395 A141865

Adjacent sequences: A222959 A222960 A222961 * A222963 A222964 A222965

Keyword

nonn,base,easy

Author

Vincenzo Librandi, Mar 18 2013

Extensions

Edited by Bruno Berselli, Mar 22 2013

Status

approved