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Search: id:A002385
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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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+0
104
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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; listen)
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OFFSET
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1,1
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COMMENT
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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
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REFERENCES
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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
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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, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Integer Sequence Primes
Wikipedia, Palindromic prime
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MAPLE
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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
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Select[ Prime[ Range[ 2100 ] ], IntegerDigits[ # ] == Reverse[ IntegerDigits[ # ] ] & ]
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CROSSREFS
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A007500 = this sequence union A006567.
Cf. A016041, A029732, A117697.
Sequence in context: A052480 A083137 A077652 this_sequence A069217 A083139 A088562
Adjacent sequences: A002382 A002383 A002384 this_sequence A002386 A002387 A002388
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KEYWORD
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nonn,base,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Oct 25 2000
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