A099744 Palindromes n such that 10n01 is a prime.

3, 5, 6, 222, 282, 353, 434, 555, 626, 656, 747, 828, 858, 929, 939, 10301, 10601, 11411, 11711, 12821, 12921, 13431, 13731, 14141, 14241, 14741, 15951, 16161, 17171, 17771, 18381, 18981, 19191, 19491, 19991, 20402, 20702, 22022, 22322

Offset: 1

Author

N. J. A. Sloane, Nov 19 2004

Keywords

• nonn
• easy
• base

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002113, A099746, A032672, A099720, A100026, A100027.

Programs

Maple

read transforms; pal:=[]; for n from 0 to 8000 do if digrev(n) = n then pal:=[op(pal),n]; fi; od:
t0:=[]; u0:=[]; for n from 1 to nops(pal) do m:=pal[n]; p0:="10"; p1:="01"; t1:=cat(p0,m,p1); t1:=convert(t1,decimal,10); if isprime(t1) then t0:=[op(t0),m]; u0:=[op(u0),t1]; fi; od: t0; # u0 gives A099746.

Mathematica

p = Select[ Range[ 22322], # == FromDigits[ Reverse[ IntegerDigits[ # ]]] &]; Select[p, PrimeQ[ FromDigits[ Join[{1, 0}, IntegerDigits[ # ], {0, 1}]]] &] (* Robert G. Wilson v, Nov 20 2004 *)
Select[Range[23000],PalindromeQ[#]&&PrimeQ[FromDigits[Join[{1,0},IntegerDigits[ #],{0,1}]]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 26 2021 *)

Extensions

More terms from Robert G. Wilson v, Nov 19 2004