A168417 - OEIS

%I #4 Jan 21 2013 09:04:44

%S 3,13,103,109,139,163,181,211,379,457,463,1021,1087,1123,1201,1249,

%T 1303,1381,1579,1597,1609,1699,1861,1873,1987,2011,2029,2053,2143,

%U 2221,2281,2341,2473,2503,2557,2731,2857,3061,3067,3217,3253,3271,3319,3331,3517

%N Primes q for which 1 concatenated with q^3 (A168327) is prime.

%C It is conjectured that this sequence is infinite.

%D Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980

%D Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005

%e (1) "1 3^3"=10^2+3^3=127=prime(31) gives a(1)=3=prime(2)

%e (2) "1 103^3"=10^7+103^3=11092727=prime(732258) gives a(3)=103=prime(27)

%t Select[Prime[Range[500]],PrimeQ[FromDigits[Join[{1},IntegerDigits[ #^3]]]]&] (* _Harvey P. Dale_, Jan 21 2013 *)

%Y A168147 Primes of the form p = 1 + 10*n^3 for a natural number n

%Y A168327 Primes of concatenated form p= "1 n^3"

%Y A168375 Natural numbers n for which the concatenation p= "1 n^3" is prime

%K nonn,base

%O 1,1

%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 25 2009

%E Edited and extended by _Charles R Greathouse IV_, Apr 23 2010