|
| |
|
|
A155973
|
|
Smallest x such that p(n+1)x^n+p(n)x^(n-1)+p(n-1)x^(n-2)+...+p(2)x^1 + 2x^0 evaluates to an odd prime.
|
|
0
| |
|
|
1, 1, 1, 11, 23, 1, 1, 75, 29, 27, 159, 27, 107, 179, 63, 93, 11, 153, 153, 197, 35, 31, 227, 297, 33, 1, 133, 1, 3, 173, 153, 299, 5, 51, 151, 1, 131, 1
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,4
|
|
|
COMMENTS
| Conjecture: The number of 1's in this sequence is infinite. Also a(n) = 1 is
sequence A013918 or the sum of the first n primes is prime. 2 is the only
prime sum for an odd n. n > 1 is even for all prime sums of the first n
primes.
|
|
|
FORMULA
| p(n) denotes the n-th prime number. primenomial(n) denotes the n-th degree
polynomial whose coefficients are the decreasing prime numbers from p(n+1)
to p(1).
|
|
|
EXAMPLE
| For n=5, primenomial(5)=
p(6)x^5+p(5)x^4+p(4)x^3+p(3)x^2+p(2)x^1+p(1)x^0 =
13x^5+11x^4+7x^3+5x^2+3x+2. The first x such that primenomial(5) is an odd
prime is 1, the 3rd entry in the sequence.
|
|
|
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 ); )) }
|
|
|
CROSSREFS
| Sequence in context: A094620 A077431 A118133 * A180481 A110044 A032663
Adjacent sequences: A155970 A155971 A155972 * A155974 A155975 A155976
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Cino Hilliard (hillcino368(AT)hotmail.com), Jan 31 2009
|
| |
|
|
