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A076609 Palindromic numbers with prime middle digit. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 16:25 EDT 2021. Contains 348091 sequences. (Running on oeis4.)