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Search: id:A155973
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| A155973 |
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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. |
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1
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| 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; listen)
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OFFSET
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1,4
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COMMENT
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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.
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FORMULA
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p(n) denotes the nth prime number. primenomial(n) denotes the nth degree
polynomial whose coefficients are the decreasing prime numbers from p(n+1)
to p(1).
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EXAMPLE
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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.
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PROGRAM
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(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 ); )) }
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CROSSREFS
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Sequence in context: A094620 A077431 A118133 this_sequence A110044 A032663 A119815
Adjacent sequences: A155970 A155971 A155972 this_sequence A155974 A155975 A155976
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Jan 31 2009
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