This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A050251 Number of palindromic primes less than 10^n. 4
 4, 5, 20, 20, 113, 113, 781, 781, 5953, 5953, 47995, 47995, 401696, 401696, 3438339, 3438339, 30483565, 30483565, 269577430, 269577430, 2427668363, 2427668363, 22170468927, 22170468927 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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, 11. - Martin Renner, Apr 15 2006 LINKS P. De Geest, World!Of Palindromic Primes, Page 1 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. FORMULA a(n) ~ A070199(n)/log(10^n) = 1/log(10^n)*Sum {k=1..n} 9*10^floor[(k-1)/2]. - Robert G. Wilson v, May 31 2009 PROG (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 def A050251(n): ....if n == 0: ........return 4 ....else: ........c = 1 ........for i in paloddgen(n//2+1): ............if isprime(i): ................c += 1 ........return c # Chai Wah Wu, Jan 05 2015 CROSSREFS Partial sums of A016115. Cf. A002113 (palindromes), A002385 (palindromic primes). Sequence in context: A042835 A193964 A099897 * A125995 A080610 A047175 Adjacent sequences:  A050248 A050249 A050250 * A050252 A050253 A050254 KEYWORD nonn,hard,nice,base,more AUTHOR EXTENSIONS More terms from Patrick De Geest, Aug 01 1999 2 more terms from Shyam Sunder Gupta, Feb 12 2006 2 more terms from Shyam Sunder Gupta, Mar 13 2009 a(22)-a(23) from Shyam Sunder Gupta, Oct 05 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 16 18:09 EST 2018. Contains 318188 sequences. (Running on oeis4.)