cp's OEIS Frontend

A308238 Nonprimes k such that k^10 + k^9 + k^8 + k^7 + k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 is prime.

%I A308238 #44 Sep 08 2022 08:46:21
%S A308238 1,20,21,30,60,86,172,195,212,224,258,268,272,319,339,355,365,366,390,
%T A308238 398,414,480,504,534,539,543,567,592,626,654,735,756,766,770,778,806,
%U A308238 812,874,943,973,1003,1036,1040,1065,1194,1210,1239,1243,1264,1309,1311
%N A308238 Nonprimes k such that k^10 + k^9 + k^8 + k^7 + k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 is prime.
%C A308238 A240693 Union {this sequence} = A162862.
%C A308238 The corresponding prime numbers, (11111111111)_k, are Brazilian primes and belong to A085104 and A285017 (except 11).
%e A308238 (11111111111)_20 = (20^11 - 1)/19 = 10778947368421 is prime, thus 20 is a term.
%p A308238 filter:= n -> not isprime(n) and isprime((n^11-1)/(n-1)) : select(filter, [$2..5000]);
%t A308238 Select[Range@ 1320, And[! PrimeQ@ #, PrimeQ@ Total[#^Range[0, 10]]] &] (* _Michael De Vlieger_, Jun 09 2019 *)
%o A308238 (Magma) [1] cat [n:n in [2..1500]|not IsPrime(n) and IsPrime(Floor((n^11-1)/(n-1)))]; // _Marius A. Burtea_, May 16 2019
%o A308238 (PARI) isok(n) = !isprime(n) && isprime(polcyclo(11, n)); \\ _Michel Marcus_, May 19 2019
%Y A308238 Cf. A162861, A162862, A240693, A286301.
%Y A308238 Intersection of A064108 and A285017.
%Y A308238 Similar to A182253 for k^2+k+1, A286094 for k^4+k^3+k^2+k+1, A288939 for k^6+k^5+k^4+k^3+k^2+k+1.
%K A308238 nonn
%O A308238 1,2
%A A308238 _Bernard Schott_, May 16 2019