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A002385
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Palindromic primes: prime numbers whose decimal expansion is a palindrome.
(Formerly M0670 N0247)
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134
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2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741, 15451, 15551, 16061, 16361, 16561, 16661, 17471, 17971, 18181
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Every palindrome with an even number of digits is divisible by 11, so 11 is the only member of the sequence with an even number of digits. - David Wasserman (wasserma(AT)spawar.navy.mil), Sep 09 2004
This holds in any number base A006093(n), n>1. - Lekraj Beedassy (blekraj(AT)yahoo.com), Mar 07 2005
Subsequence of A188650; A188649(a(n)) = a(n); see A033620 for multiplicative closure. [Reinhard Zumkeller, Apr 11 2011]
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 228.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Attila Olah, Table of n, a(n) for n=1..100197
K. S. Brown, On General Palindromic Numbers
P. De Geest, World!Of Palindromic Primes
I. Peterson, Math Trek, Palindromic Primes
M. Shafer, First 401066 Palprimes [Broken link]
Eric Weisstein's World of Mathematics, Palindromic Number
Eric Weisstein's World of Mathematics, Palindromic Prime
Eric Weisstein's World of Mathematics, Integer Sequence Primes
Wikipedia, Palindromic prime
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FORMULA
| Intersection of A000040 (primes) and A002113 (palindromes).
A010051(a(n)) * A136522(a(n)) = 1. [Reinhard Zumkeller, Apr 11 2011]
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MAPLE
| ff := proc(n) local i, j, k, s, aa, nn, bb, flag; s := n; aa := convert(s, string); nn := length(aa); bb := ``; for i from nn by -1 to 1 do bb := cat(bb, substring(aa, i..i)); od; flag := 0; for j from 1 to nn do if substring(aa, j..j)<>substring(bb, j..j) then flag := 1 fi; od; RETURN(flag); end; gg := proc(i) if ff(ithprime(i)) = 0 then RETURN(ithprime(i)) fi end;
rev:=proc(n) local nn, nnn: nn:=convert(n, base, 10): add(nn[nops(nn)+1-j]*10^(j-1), j=1..nops(nn)) end: a:=proc(n) if n=rev(n) and isprime(n)=true then n else fi end: seq(a(n), n=1..20000); # rev is a Maple program to revert a number - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 25 2007
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MATHEMATICA
| Select[ Prime[ Range[ 2100 ] ], IntegerDigits[ # ] == Reverse[ IntegerDigits[ # ] ] & ]
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PROG
| (Haskell)
a002385 n = a002385_list !! (n-1)
a002385_list = filter ((== 1) . a136522) a000040_list
-- Reinhard Zumkeller, Apr 11 2011
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CROSSREFS
| A007500 = this sequence union A006567.
Cf. A016041, A029732, A117697.
Sequence in context: A077652 * A069217 A083139 A088562 A083712 A082806
Adjacent sequences: A002382 A002383 A002384 * A002386 A002387 A002388
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KEYWORD
| nonn,base,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Oct 25 2000
Comment from A006093 moved here by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 03 2009
Mentioned the sequence A006093 in my comment, previously omitted by mistake Lekraj Beedassy (blekraj(AT)yahoo.com), Dec 06 2009
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