A155973 Smallest x such that prime(2n)x^(2n-1) + prime(2n-1)x^(2n-2) + prime(2n-2)x^(2n-3) +...+ prime(2)x^1 + 2x^0 evaluates to an odd prime.

1, 1, 1, 11, 23, 1, 1, 75, 29, 27, 159, 27, 107, 179, 63, 93, 675, 593, 11, 1299, 153, 153, 197, 35, 31, 227, 297, 439, 33, 1, 133, 1, 3, 1071, 173, 153, 299, 5, 1443, 1275, 611, 1809, 941, 669, 537, 51, 151, 1, 131, 1, 1, 343, 199, 1, 279, 3, 1, 439, 597, 453, 1, 1, 1187, 391

Offset: 1

Author

Cino Hilliard, Jan 31 2009

Keywords

• nonn

Comments

Conjecture: The number of 1's in this sequence is infinite.

a(n) = 1 if and only if 2n is in A013916.

Examples

			n=1: 3x + 2, prime for x = 1, so a(1) = 1.
n=2: 7x^3 + 5x^2 + 3x + 2, prime for x = 1, so a(2) = 1.
n=3: 13x^5 + 11x^4 + 7x^3 + 5x^2 + 3x + 2, prime for x = 1, so a(3) = 1.
n=4: 19x^7 + 17x^6 + 13x^5 + 11x^4 + 7x^3 + 5x^2 + 3x + 2, prime for x = 11, so a(4) = 11.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..200

Programs

PARI

primenomial(n) = { ct=0; sr=0; p=0; d=0; d1=0; forstep(m=1,n,2, for(x=0,n,y=2; for(j=2,m+1, p = prime(j); y+=x^(j-1)*p; );
if(y>2&&ispseudoprime(y),ct+=1; print1(x",");break ); )) }

PARI

a(n)=my(P=Polrev(primes(2*n)),k=1);while(!ispseudoprime(subst(P, 'x, k)), k+=2); k \\ Charles R Greathouse IV, Jan 15 2013

Extensions

a(39)-a(64) from Charles R Greathouse IV, Jan 17 2013