A210534 - OEIS

%I #32 Jun 11 2019 19:47:20

%S 331,661,881,991,12211,14411,15511,20021,21121,23321,24421,29921,

%T 33331,35531,41141,45541,47741,50051,51151,57751,59951,63361,71171,

%U 72271,74471,75571,81181,84481,99991,1022011,1255211,1299211,1311311,1344311,1355311

%N Primes formed by concatenating palindromes having even number of digits with 1.

%C Analogous to A210511, except that the second n is digit reversed. If the first (leftmost) n were reversed, we would have problems with trailing zeros becoming leading zeros, which get removed in OEIS formatting. That is a slightly different sequence is given by the formula primes of the form n concatenated with A004086(n) concatenated with "1"; or Primes of form a(n) = (n*10^A055642(n)+A004086(n)) concatenated with "1".

%C There are 190 terms up to all 6-digit palindromes (i.e., 7-digit primes), 1452 terms up to all 8-digit palindromes (i.e., 9-digit primes), and 11724 terms up to all 10-digit palindromes (i.e., 11-digit primes). - _Harvey P. Dale_, Jul 06 2018

%H Harvey P. Dale, <a href="/A210534/b210534.txt">Table of n, a(n) for n = 1..1452</a>

%e a(18) = 50 concatenated with R(50)=05 concatenated with "1" = 50051, which is prime.

%p fulldigRev := proc(n)

%p     local digs ;

%p     digs := convert(n,base,10) ;

%p     [op(ListTools[Reverse](digs)),op(digs)] ;

%p end proc:

%p for n from 1 to 150 do

%p     r := [1,op(fulldigRev(n))] ;

%p     p := add(op(i,r)*10^(i-1),i=1..nops(r)) ;

%p     if isprime(p) then

%p         printf("%d,",p);

%p     end if;

%p end do: # _R. J. Mathar_, Feb 21 2013

%t 10#+1&/@Select[Table[FromDigits[Join[IntegerDigits[n],Reverse[ IntegerDigits[ n]]]],{n,9999}],PrimeQ[10#+1]&](* _Harvey P. Dale_, Jul 06 2018 *)

%t 10#+1&/@Select[Flatten[Table[Range[10^n,10^(n+1)],{n,1,5,2}]], PalindromeQ[ #] && PrimeQ[10#+1]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 11 2019 *)

%Y Cf. A000040, A004086, A210511.

%K nonn,base,easy

%O 1,1

%A _Jonathan Vos Post_, Jan 30 2013