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A158232
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Numbers which yield primes when "13" is prefixed or appended: N natural number is a member of the sequence, if P="13N" (prefixed 13) and A="N13" (appended 13) are prime.
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11
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1, 19, 21, 27, 61, 103, 121, 127, 147, 159, 177, 183, 187, 217, 241, 259, 267, 327, 331, 337, 367, 381, 411, 477, 523, 553, 567, 577, 591, 633, 681, 687, 693, 709, 723, 759, 807, 829, 873, 903, 931, 997, 1009, 1011, 1041, 1059, 1129, 1149, 1213, 1231, 1251
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OFFSET
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1,2
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COMMENTS
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It is conjectured and numerically examined that sequences of this type are infinite.
It is also conjectured that an infinite number of primes are terms of the sequence; first 20 primes are: 19, 61, 103, 127, 241, 331, 337, 367, 523, 577, 709, 829, 997, 1009, 1129, 1213, 1381, 1489, 1543, 1627.
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REFERENCES
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A. Weil, Number theory: an approach through history, Birkhäuser, 1984.
Richard E. Crandall, Carl Pomerance, Prime Numbers, Springer 2005.
Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996.
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LINKS
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EXAMPLE
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19: 1319 and 1913 are primes => a(2)=19;
7 is not a term: 137 is prime but 713=23 * 31 is not.
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MAPLE
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A055642 := proc(n) max(1, ilog10(n)+1) ; end proc: cat2 := proc(a, b) a*10^A055642(b)+b ; end proc: A158232 := proc(n) option remember; local a; if n = 1 then 1; else for a from procname(n-1)+1 do if isprime(cat2(13, a)) and isprime(cat2(a, 13)) then return a ; end if ; end do ; end if; end proc: seq(A158232(n), n=1..80) ; # R. J. Mathar, Nov 11 2009
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MATHEMATICA
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Select[Range[1300], And@@PrimeQ[{13 10^IntegerLength[#]+#, 100#+13}]&] (* Harvey P. Dale, May 28 2012 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 14 2009
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STATUS
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approved
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