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A050251
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Number of palindromic primes less than 10^n.
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4
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0, 4, 5, 20, 20, 113, 113, 781, 781, 5953, 5953, 47995, 47995, 401696, 401696, 3438339, 3438339, 30483565, 30483565, 269577430, 269577430, 2427668363, 2427668363, 22170468927, 22170468927
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OFFSET
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0,2
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COMMENTS
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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, 11. - Martin Renner, Apr 15 2006
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LINKS
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FORMULA
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PROG
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(Python)
from __future__ import division
from sympy import isprime
def paloddgen(l, b=10): # generator of odd-length palindromes in base b of length <= 2*l
if l > 0:
yield 0
for x in range(1, l+1):
n = b**(x-1)
n2 = n*b
for y in range(n, n2):
k, m = y//b, 0
while k >= b:
k, r = divmod(k, b)
m = b*m + r
yield y*n + b*m + k
if n <= 1:
return 4*n
else:
c = 1
for i in paloddgen((n+1)//2):
if isprime(i):
c += 1
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CROSSREFS
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KEYWORD
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nonn,hard,nice,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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