A088579 Primes of the form n*x^n + (n-1)*x^(n-1) + . . . + x + 1 for x=2.

3, 11, 643, 425987, 1909526242005090307

Offset: 1

Author

Cino Hilliard, Nov 20 2003

Keywords

• nonn

Comments

Sum of reciprocals = 0.4257999816852453227652727311..

Next term is too large to include.

Examples

			2*2^2 + 1*2 + 1 = 11 is prime.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10 (terms 1..9 from Michel Marcus)

Crossrefs

Cf. A055469 (for x=1), A088584 (for x=3), A088583 (for x=4).

Programs

Mathematica

Select[Table[1+Sum[k 2^k, {k,n}], {n,1000}], PrimeQ] (* T. D. Noe, Nov 15 2006 *)

PARI

polypn2(n,p) = { my(x=n,y=1); for(m=1,p, y=y+m*x^m; ); return(y) }
trajpolyp(n1,k) = { my(s=0); for(x1=0,n1, y1 = polypn2(k,x1); if(isprime(y1),print1(y1, ","); s+=1.0/y1; ) ); }
trajpolyp(500,2)

Extensions

Corrected by T. D. Noe and Don Reble, Nov 15 2006