|
%I #12 May 10 2019 22:52:42
%S 1,19,21,27,61,103,121,127,147,159,177,183,187,217,241,259,267,327,
%T 331,337,367,381,411,477,523,553,567,577,591,633,681,687,693,709,723,
%U 759,807,829,873,903,931,997,1009,1011,1041,1059,1129,1149,1213,1231,1251
%N 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 It is conjectured and numerically examined that sequences of this type are infinite.
%C 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.
%D A. Weil, Number theory: an approach through history, Birkhäuser, 1984.
%D Richard E. Crandall, Carl Pomerance, Prime Numbers, Springer 2005.
%D Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996.
%H Harvey P. Dale, <a href="/A158232/b158232.txt">Table of n, a(n) for n = 1..1000</a>
%e 19: 1319 and 1913 are primes => a(2)=19;
%e 7 is not a term: 137 is prime but 713=23 * 31 is not.
%p 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
%t Select[Range[1300],And@@PrimeQ[{13 10^IntegerLength[#]+#,100#+13}]&] (* _Harvey P. Dale_, May 28 2012 *)
%Y Cf. A157772.
%K nonn,base
%O 1,2
%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 14 2009
|
