A168147 - OEIS

%I #19 Sep 08 2022 08:45:48

%S 11,271,641,2161,33751,40961,58321,138241,196831,270001,297911,466561,

%T 506531,795071,1326511,1406081,1851931,2160001,3890171,4218751,

%U 5314411,5513681,6585031,7290001,8043571,11910161,12597121,12950291,14815441

%N Primes of the form 10*n^3 + 1.

%C (1) These primes all with end digit 1=1^3 are concatenations of two CUBIC numbers: "n^3 1".

%C (2) It is conjectured that the sequence is infinite.

%C (3) It is an open problem if 3 consecutive naturals n exist which give such a prime.

%C No three such integers exist, as every n = 2 (mod 3) yields 10n^3 + 1 = 0 (mod 3). - _Charles R Greathouse IV_, Apr 24 2010

%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

%H Vincenzo Librandi, <a href="/A168147/b168147.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = 10*A168219(n)^3 + 1.  \\ _M. F. Hasler_, Jul 24 2011

%t Select[Table[10*n^3+1,{n,1000}],PrimeQ] (* _Vincenzo Librandi_, Aug 01 2012 *)

%o (PARI) for(n=1,2e2, isprime(n^3*10+1) && print1(n^3*10+1", "))  \\ _M. F. Hasler_, Jul 24 2011

%o (Magma) [ a: n in [1..150] | IsPrime(a) where a is 10*n^3+1 ]; // _Vincenzo Librandi_, Jul 25 2011

%Y Cf. A030430 (primes of the form 10*n+1).

%Y Cf. A167535 (concatenation of two square numbers which give a prime).

%Y See A168219 for the numbers n.

%K nonn,base,easy

%O 1,1

%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 19 2009