A088550 Primes of the form n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.

7, 127, 1093, 19531, 55987, 5229043, 8108731, 25646167, 321272407, 917087137, 3092313043, 4201025641, 9684836827, 31401724537, 47446779661, 52379047267, 83925549247, 100343116693, 141276239497, 153436090543, 265462278481

Offset: 1

Author

Cino Hilliard, Nov 17 2003

Keywords

• nonn
• easy

Comments

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

Examples

			a(3) = 1093 = 3^6 + 3^5 + 3^4 + 3^3 + 3^2 + 3 + 1 is prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38.
• Bernard Schott, Les nombres brésiliens, Reprinted from Quadrature, no. 76, avril-juin 2010, pages 30-38, included here with permission from the editors of Quadrature.

Crossrefs

Cf. A085104, A100330.

Programs

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

Maple

A088550 := proc(n)
    numtheory[cyclotomic](7,A100330(n)) ;
end proc:
seq(A088550(n),n=1..30) ;

Mathematica

Select[Table[n^6 + n^5 + n^4 + n^3 + n^2 + n + 1, {n, 100}], PrimeQ] (* Alonso del Arte, Feb 07 2014 *)
Select[Table[Total[n^Range[0,6]],{n,100}],PrimeQ] (* Harvey P. Dale, Aug 13 2024 *)

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",")); ) }