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 A158232 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 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 1) It is conjectured and numerically examined that sequences of this type are infinite 2) It is also conjectured, that an infinite number of primes are member 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 REFERENCES A. Weil, Number theory: an approach through history, Birkhaeuser 1984 Richard E. Crandall, Carl Pomerance, Prime Numbers, Springer 2005 Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE examples: 1) 19: 1319 and 1913 are primes => a(2)=19 2) 7 is no member: 137 is prime but 713=23 x 31 is not MAPLE 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) ; [From R. J. Mathar, Nov 11 2009] MATHEMATICA Select[Range[1300], And@@PrimeQ[{13 10^IntegerLength[#]+#, 100#+13}]&] (* Harvey P. Dale, May 28 2012 *) CROSSREFS Cf. A157772. Sequence in context: A089837 A020347 A054864 * A178889 A167998 A050714 Adjacent sequences:  A158229 A158230 A158231 * A158233 A158234 A158235 KEYWORD nonn,base AUTHOR Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 14 2009 STATUS approved

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