Search: id:A158232
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%I A158232
%S A158232 1,19,21,27,61,103,121,127,147,159,177,183,187,217,241,259,267,327,331,
%T A158232 337,367,381,411,477,523,553,567,577,591,633,681,687,693,709,723,759,
%U A158232 807,829,873,903,931,997,1009,1011,1041,1059,1129,1149,1213,1231,1251
%N 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
%C A158232 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
%D A158232 A. Weil, Number theory: an approach through history, Birkhaeuser 1984
%D A158232 Richard E. Crandall, Carl Pomerance, Prime Numbers, Springer 2005
%D A158232 Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996
%e A158232 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
%p A158232 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 (mathar(AT)strw.leidenuniv.nl), 
               Nov 11 2009]
%Y A158232 A157772
%Y A158232 Sequence in context: A089837 A020347 A054864 this_sequence A050714 A113868 
               A023152
%Y A158232 Adjacent sequences: A158229 A158230 A158231 this_sequence A158233 A158234 
               A158235
%K A158232 nonn,new
%O A158232 1,2
%A A158232 Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 14 2009

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