

A136646


Primes that give find root imaginary results for: z1 = 1/2  4*I*Pi*x; z2 = 1  8*I*Pi*x; 1 + 2 x^z1 + x^z2 == 0; with Im[x]<0.05. The resulting root share value of the Zeta[root] being near one.


0



89, 619, 877, 1193, 1319, 1481, 1747, 2437, 2447, 2521, 2647, 3163, 3371, 3449, 3469, 5711, 6007, 6089, 6659, 7001, 7121
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OFFSET

1,1


COMMENTS

This result is my second try at this type of experiment. I had this idea of looking at the product elements in the zeta product as limiting near primes.
pe[n]=1/(1Prime[n]^(z)) ; Limit[Pe[n],x>Prime[n]+Delta1+I*Delta2]=0, where z=1/2+i*4*Pi*Prime[n].
I solved it down to an equation in n x and then, I looked a near specific primes. Two types show up: Normal Riemannian 1/2 primes on a curve and second type that are attracted to one instead.
There seems to be a spectral effect in the Delta2 values. The curve ZDelta2 go to a lower limit and the second types are all well below that limiting curve.


LINKS

Table of n, a(n) for n=1..21.


FORMULA

x start at Prime[n]: when the equation z1 = 1/2  4*I*Pi*x; z2 = 1  8*I*Pi*x; 1 + 2 x^z1 + x^z2 == 0; has a root with Im[x]<0.05. the starting prime is reported out.


MATHEMATICA

z1 = 1/2  4*I*Pi*x; z2 = 1  8*I*Pi*x; a1 = Flatten[Table[If[(Im[x] /. FindRoot[1 + 2 x^z1 + x^z2 == 0, {x, Prime[n]}]) < 0.05, Prime[n], {}], {n, 1, 1000}]]


CROSSREFS

Sequence in context: A176634 A224740 A028472 * A142566 A063654 A308801
Adjacent sequences: A136643 A136644 A136645 * A136647 A136648 A136649


KEYWORD

nonn,uned


AUTHOR

Roger L. Bagula, Apr 14 2008


STATUS

approved



