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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, 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 (list; graph; refs; listen; history; text; internal format)
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: A077431 A118133 A225186 * A253684 A180481 A110044

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

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Last modified August 12 12:09 EDT 2020. Contains 336439 sequences. (Running on oeis4.)