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%I A088550 #31 Aug 13 2024 19:11:10
%S A088550 7,127,1093,19531,55987,5229043,8108731,25646167,321272407,917087137,
%T A088550 3092313043,4201025641,9684836827,31401724537,47446779661,52379047267,
%U A088550 83925549247,100343116693,141276239497,153436090543,265462278481
%N A088550 Primes of the form n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.
%C A088550 These numbers, starting with 127, are repunit primes 1111111_n in a base n >= 2, so except 7, they are all Brazilian primes belonging to A085104. In fact, 7 = 111_2 is also Brazilian by this other way. (See Links "Les nombres brésiliens", § V.4 -§ V.5.) A088550 is generated by the bases n present in A100330. - _Bernard Schott_, Dec 20 2012
%H A088550 Vincenzo Librandi, <a href="/A088550/b088550.txt">Table of n, a(n) for n = 1..1000</a>
%H A088550 Bernard Schott, <a href="http://quadrature.info/">Les nombres brésiliens</a>, Quadrature, no. 76, avril-juin 2010, pages 30-38.
%H A088550 Bernard Schott, <a href="/A125134/a125134.pdf">Les nombres brésiliens</a>, Reprinted from Quadrature, no. 76, avril-juin 2010, pages 30-38, included here with permission from the editors of Quadrature.
%e A088550 a(3) = 1093 = 3^6 + 3^5 + 3^4 + 3^3 + 3^2 + 3 + 1 is prime.
%p A088550 A088550 := proc(n)
%p A088550     numtheory[cyclotomic](7,A100330(n)) ;
%p A088550 end proc:
%p A088550 seq(A088550(n),n=1..30) ;
%t A088550 Select[Table[n^6 + n^5 + n^4 + n^3 + n^2 + n + 1, {n, 100}], PrimeQ] (* _Alonso del Arte_, Feb 07 2014 *)
%t A088550 Select[Table[Total[n^Range[0,6]],{n,100}],PrimeQ] (* _Harvey P. Dale_, Aug 13 2024 *)
%o A088550 (PARI) polypn(n,p) = { for(x=1,n, if(p%2,y=2,y=1); for(m=1,p, y=y+x^m; ); if(isprime(y),print1(y",")); ) }
%o A088550 (Magma) [a: n in [0..100] | IsPrime(a) where a is 1+n+n^2+n^3+n^4+n^5+n^6] ; // _Vincenzo Librandi_, Jul 14 2012
%Y A088550 Cf. A085104, A100330.
%K A088550 nonn,easy
%O A088550 1,1
%A A088550 _Cino Hilliard_, Nov 17 2003

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