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

1,4

Comments

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

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

Links

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

Example

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.

Prog

(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

Crossrefs

Sequence in context: A118133 A345404 A225186 * A351849 A253684 A364165

Adjacent sequences: A155970 A155971 A155972 * A155974 A155975 A155976

Keyword

nonn

Author

Cino Hilliard, Jan 31 2009

Extensions

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

Status

approved