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Primes of the form n*x^n + (n-1)*x^(n-1) + . . . + x + 1 for x=2.
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%I #22 Aug 25 2024 09:56:33

%S 3,11,643,425987,1909526242005090307

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

%C Sum of reciprocals = 0.4257999816852453227652727311..

%C Next term is too large to include.

%H Michel Marcus, <a href="/A088579/b088579.txt">Table of n, a(n) for n = 1..9</a>

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

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

%o (PARI) polypn2(n,p) = { my(x=n,y=1); for(m=1,p, y=y+m*x^m; ); return(y) }

%o trajpolyp(n1,k) = { my(s=0); for(x1=0,n1, y1 = polypn2(k,x1); if(isprime(y1),print1(y1, ","); s+=1.0/y1; ) ); }

%o trajpolyp(500,2)

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

%K nonn

%O 1,1

%A _Cino Hilliard_, Nov 20 2003

%E Corrected by _T. D. Noe_ and _Don Reble_, Nov 15 2006