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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

Table of n, a(n) for n=1..24.

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

CROSSREFS

Cf. A002113 (palindromes), A002385 (palindromic primes), A040025 (bisection), A050251 (partial sums).

Sequence in context: A257501 A096644 A145829 * A164794 A226478 A293129

Adjacent sequences:  A016112 A016113 A016114 * A016116 A016117 A016118

KEYWORD

nonn,hard,base,more,changed

AUTHOR

Robert G. Wilson v

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 September 23 05:43 EDT 2018. Contains 315273 sequences. (Running on oeis4.)