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

1,1

Comments

There are no such with an even number of digits.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A032350.

Sequence in context: A086107 A046713 A119835 * A117059 A117058 A067173

Adjacent sequences: A076606 A076607 A076608 * A076610 A076611 A076612

Keyword

easy,nonn,base

Author

Jani Melik, Oct 21 2002

Status

approved