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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

%I

%S 1,1,1,11,23,1,1,75,29,27,159,27,107,179,63,93,675,593,11,1299,153,

%T 153,197,35,31,227,297,439,33,1,133,1,3,1071,173,153,299,5,1443,1275,

%U 611,1809,941,669,537,51,151,1,131,1,1,343,199,1,279,3,1,439,597,453,1,1,1187,391

%N 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.

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

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

%H Charles R Greathouse IV, <a href="/A155973/b155973.txt">Table of n, a(n) for n = 1..200</a>

%e n=1: 3x + 2, prime for x = 1, so a(1) = 1.

%e n=2: 7x^3 + 5x^2 + 3x + 2, prime for x = 1, so a(2) = 1.

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

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

%o (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; );

%o if(y>2&&ispseudoprime(y),ct+=1; print1(x",");break ); )) }

%o (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

%K nonn

%O 1,4

%A _Cino Hilliard_, Jan 31 2009

%E a(39)-a(64) from _Charles R Greathouse IV_, Jan 17 2013

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Last modified September 28 05:33 EDT 2020. Contains 337392 sequences. (Running on oeis4.)