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 A016115 Number of prime palindromes with n digits. 6
 4, 1, 15, 0, 93, 0, 668, 0, 5172, 0, 42042, 0, 353701, 0, 3036643, 0, 27045226, 0, 239093865, 0, 2158090933, 0, 19742800564, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Every palindrome with an even number of digits is divisible by 11 and therefore is composite (not prime). Hence there is only one palindromic prime with an even number of digits, namely 11 itself. - Martin Renner, Apr 15 2006 LINKS K. S. Brown, On General Palindromic Numbers P. De Geest, World!Of Palindromic Primes Shyam Sunder Gupta, Palindromic Primes up to 10^19. Shyam Sunder Gupta, Palindromic Primes up to 10^23. Eric Weisstein's World of Mathematics, Palindromic Prime. MAPLE # A016115 Gets numbers of base-10 palindromic primes with exactly d digits, 1 <= d <= 13 (say), in the list "lis" lis:=[4, 1]; for d from 3 to 13 do if d::even then     lis:=[op(lis), 0]; else     m:= (d-1)/2:     Res2 := [seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1)]:     ct:=0; for x in Res2 do if isprime(x) then ct:=ct+1; fi: od:     lis:=[op(lis), ct]; fi: lprint(d, lis); od: lis; # N. J. A. Sloane, Oct 18 2015 MATHEMATICA A016115[n_] := Module[{i}, If[EvenQ[n] && n > 2, Return[0]]; Return[Length[Select[Range[10^(n - 1), 10^n - 1], # == IntegerReverse[#] && PrimeQ[#] &]]]]; Table[A016115[n], {n, 6}] (* Robert Price, May 25 2019 *) (* -OR-  A less straight forward implementation, but more efficient in that the palindromes are constructed instead of testing every number in the range. *) A016115[n_] := Module[{c, f, t0, t1},    If[n == 2, Return[1]];    If[EvenQ[n], Return[0]];    c = 0; t0 = 10^((n - 1)/2); t1 = t0*10;    For[f = t0, f < t1, f++,     If[n != 1 && MemberQ[{2, 4, 5, 6, 8}, Floor[f/t0]], f = f + t0 - 1; Continue[]];     If[PrimeQ[f*t0 + IntegerReverse[Floor[f/10]]], c++]]; Return[c]]; Table[A016115[n], {n, 1, 12}] (* Robert Price, May 25 2019 *) CROSSREFS Cf. A002113 (palindromes), A002385 (palindromic primes), A040025 (bisection), A050251 (partial sums). Sequence in context: A257501 A096644 A145829 * A164794 A226478 A328235 Adjacent sequences:  A016112 A016113 A016114 * A016116 A016117 A016118 KEYWORD nonn,hard,base,more AUTHOR EXTENSIONS Corrected and extended by Patrick De Geest, Jun 15 1998 a(17) = 27045226 was found in collaboration with Martin Eibl (M.EIBL(AT)LINK-R.de), Carlos Rivera, Warut Roonguthai a(19) from Shyam Sunder Gupta, Feb 12 2006 a(21)-a(22) from Shyam Sunder Gupta, Mar 13 2009 a(23)-a(24) from Shyam Sunder Gupta, Oct 05 2013 STATUS approved

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Last modified April 10 08:06 EDT 2021. Contains 342843 sequences. (Running on oeis4.)