A076609 Palindromic numbers with prime middle digit.
2, 3, 5, 7, 121, 131, 151, 171, 222, 232, 252, 272, 323, 333, 353, 373, 424, 434, 454, 474, 525, 535, 555, 575, 626, 636, 656, 676, 727, 737, 757, 777, 828, 838, 858, 878, 929, 939, 959, 979, 10201, 10301, 10501, 10701, 11211, 11311, 11511, 11711, 12221
Offset: 1
Examples
a(12)=272=2^4*17 is palindromic number and its middle digit 7 is prime, a(13)=323=17*19 is palindromic number and its middle digit 2 is prime, a(14)=333=3^2*37 is palindromic number and its middle digit 3 is prime.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
-
Maple
ts_numprapal := proc(n) local ad,adr,midigit; ad := convert(n,base,10): adr := ListTools[Reverse](ad): if nops(ad) mod 2 = 0 then return 1; fi; midigit := op( (nops(ad)+1)/2,ad ): if (isprime( midigit )='true' and adr=ad) then return 0; else return 1; fi end: ts_num_pal := proc(i) if ts_numprapal(i) = 0 then return (i) fi end: anumpal := [seq(ts_num_pal(i), i=1..50000)]: anumpal;
-
Mathematica
pnpmdQ[n_]:=Module[{idn=IntegerDigits[n],len=IntegerLength[n]},OddQ[len] && PalindromeQ[n]&&PrimeQ[idn[[(len+1)/2]]]]; Select[Range[15000],pnpmdQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 08 2017 *)
Comments