A109627 Numbers k such that concatenation of k and its 10's complement is a palindromic prime.

91, 9091, 9271, 9451, 900991, 907291, 914581, 917281, 920971, 931861, 939061, 943651, 954541, 958141, 960931, 972721, 975421, 977221, 978121, 982711, 90027991, 90209791, 90272791, 90372691, 90381691, 90627391, 90745291, 90990091

Offset

1,1

Comments

The Mathematica code can be modified to verify that the included list is a complete listing of the sequence such that a(n) < 100000000. - Keith Schneider (schneidk(AT)unc.edu), May 20 2007, May 21 2007

Links

Robert Israel, Table of n, a(n) for n = 1..10000 (first 108 terms from Keith Schneider)

Example

a(3)=9271 because 10^4-9271 = 729 and concatenating produces the palprime 9271729.

Maple

f:= proc(x) local i, L;
    L:= convert(x, base, 10);
    10^nops(L)*x + add((9-L[-i])*10^(i-1), i=1..nops(L))+1;
end proc:
filter:= proc(n) local  np;
   np:= n * 10^(ilog10(n)) + 10^(1+ilog10(n))-n;
   isprime(np);
end proc:
select(filter, [5, 91, seq(seq(f(9*10^d+j), j=0..9*10^(d-1)-1), d=1..3)]); # Robert Israel, May 17 2026

Mathematica

Remove[PalList, PrimeList, SeqList]
PalList[n_] := PalList[n] = Table[FromDigits[Join[Join[{9},
PadLeft[IntegerDigits[i], n/2 - 1], Reverse[ PadLeft[IntegerDigits[ 10^(n/2 - 1) - 1 - i], n/2 - 1]], {1}], Reverse[Join[{9}, PadLeft[IntegerDigits[i], n/2 - 1], Reverse[ PadLeft[IntegerDigits[10^(n/2 - 1) - 1 - i], n/2 - 1]]]]]], { i, 0, 10^(n/2 - 1) - 10^(n/2 - 2) - 1}];
PrimeList[n_] := PrimeList[n] = Delete[Union[Table[If[ PrimeQ[PalList[n][[ i]]], PalList[n][[i]]], {i, 1, Length[PalList[n]]}]], -1];
SeqList[2] = {91};
SeqList[n_] := SeqList[n] = Table[FromDigits[IntegerDigits[ PrimeList[n][[i]]][[Range[n]]]], {i, 1, Length[PrimeList[n]]}];
TheList = Join[SeqList[2], SeqList[4], SeqList[6], SeqList[8],
SeqList[10], SeqList[12], SeqList[14]]; TheList // TableForm
Length[TheList] (* Keith Schneider, May 21 2007 *)
palprQ[n_]:=Module[{c=10^IntegerLength[n]-n, t}, t=n 10^IntegerLength[c]+c; PrimeQ[t]&&PalindromeQ[t]]; Select[Range[91*10^6], palprQ] (* Harvey P. Dale, Aug 09 2025 *)

Crossrefs

Subsequence of A109625.

Sequence in context: A202564 A006244 A054216 * A095372 A165154 A015261

Adjacent sequences: A109624 A109625 A109626 * A109628 A109629 A109630

Keyword

base,nonn

Author

Jason Earls, Aug 02 2005

Extensions

More terms from Keith Schneider (schneidk(AT)unc.edu), May 20 2007, May 21 2007

One more term from Harvey P. Dale, Aug 09 2025

Status

approved