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A210534
Primes formed by concatenating palindromes having even number of digits with 1.
1
331, 661, 881, 991, 12211, 14411, 15511, 20021, 21121, 23321, 24421, 29921, 33331, 35531, 41141, 45541, 47741, 50051, 51151, 57751, 59951, 63361, 71171, 72271, 74471, 75571, 81181, 84481, 99991, 1022011, 1255211, 1299211, 1311311, 1344311, 1355311
OFFSET
1,1
COMMENTS
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".
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
LINKS
EXAMPLE
a(18) = 50 concatenated with R(50)=05 concatenated with "1" = 50051, which is prime.
MAPLE
fulldigRev := proc(n)
local digs ;
digs := convert(n, base, 10) ;
[op(ListTools[Reverse](digs)), op(digs)] ;
end proc:
for n from 1 to 150 do
r := [1, op(fulldigRev(n))] ;
p := add(op(i, r)*10^(i-1), i=1..nops(r)) ;
if isprime(p) then
printf("%d, ", p);
end if;
end do: # R. J. Mathar, Feb 21 2013
MATHEMATICA
10#+1&/@Select[Table[FromDigits[Join[IntegerDigits[n], Reverse[ IntegerDigits[ n]]]], {n, 9999}], PrimeQ[10#+1]&](* Harvey P. Dale, Jul 06 2018 *)
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 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Jonathan Vos Post, Jan 30 2013
STATUS
approved