%I #47 Oct 29 2023 13:35:19
%S 13,47,103,181,281,547,10111,14557,22741,25873,29207,44563,48907,
%T 53453,90931,103457,110023,116791,161641,169823,178207,186793,195581,
%U 232753,242551,273157,283763,305581,316793,440023,523657,538303,568201,614563,662743
%N Primes of the form kk*k+k+1, where kk is the concatenation of k with itself.
%C 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,...
%C 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.
%H Vincenzo Librandi, <a href="/A222962/b222962.txt">Table of n, a(n) for n = 1..1000</a>
%e 22741 is in the sequence because it is prime and 22741=1515*15+15+1.
%t f[n_] := FromDigits@Flatten@IntegerDigits[{n, n}] n + n + 1; Select[Table[f[n], {n, 100}], PrimeQ] (* _Bruno Berselli_, Mar 21 2013 *)
%t Select[Table[n(n*10^IntegerLength[n]+n)+n+1,{n,100}],PrimeQ] (* _Harvey P. Dale_, Oct 29 2023 *)
%o (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
%Y Cf. A020338, A157711.
%K nonn,base,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 18 2013
%E Edited by _Bruno Berselli_, Mar 22 2013