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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 (list; graph; refs; listen; history; text; internal format)
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

Harvey P. Dale, Table of n, a(n) for n = 1..1452

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

Cf. A000040, A004086, A210511.

Sequence in context: A142763 A020373 A142601 * A210511 A142824 A038647

Adjacent sequences:  A210531 A210532 A210533 * A210535 A210536 A210537

KEYWORD

nonn,base,easy

AUTHOR

Jonathan Vos Post, Jan 30 2013

STATUS

approved

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Last modified April 9 09:59 EDT 2020. Contains 333348 sequences. (Running on oeis4.)