## hermite projection of the primes->[Fwd: SEQ FROM Roger L. Bagula]

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• ... Subject: SEQ FROM Roger L. Bagula Date: Sun, 14 Sep 2003 17:04:22 -0400 (EDT) From: Reply-To: tftn@earthlink.net To:
Message 1 of 1 , Sep 14, 2003
-------- Original Message --------
Subject: SEQ FROM Roger L. Bagula
Date: Sun, 14 Sep 2003 17:04:22 -0400 (EDT)
From: <njas@...>
To: njas@...
CC: tftn@...

The following is a copy of the email message that was sent to njas
containing the sequence you submitted.

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Subject: NEW SEQUENCE FROM Roger L. Bagula

%I A000001
%S A000001 34256905988,13833711045,3161243909,867446001,79422563,2390757,278055,8098,104,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0
%N A000001 A scaled integer projection of the Primes onto a Hermite Hilbert space of orthogonal functions by a sum.
%C A000001 This result is scaled so the smallest integer greater than zero is one. It is
the most number of basis functions (25) my computer will calculate before crashing. This result was suggested by finding that:
Sum[Exp[-n^2]*Prime[n],{n,1,infinity}]=0.791323635928514
to 200 decimals: that is it is finite and rational.
%F A000001 Hermite recursive Polynomial from Jahnke and Emde: "Tables of Functions", page 32
H[n_Integer?Positive] :=H[n] =m*H[n-1] -(n-1)* H[n-2]
H[0] = 1
H[1] = m
Table[Abs[Floor[Sum[H[n]**Exp[-m^2/2]*Prime[n],{n,1,25}]/5^5]],{m,1,50}]

%t A000001 H[n_Integer?Positive] :=H[n] =m*H[n-1] -(n-1)* H[n-2]
H[0] = 1
H[1] = m
digits=25
h[m_]=Sum[H[n]*Exp[-m^2/2]*Prime[n+1],{n,0, digits}];
Seq[m_]=Floor[N[h[m]/(5*digits^2)]];
sq=Table[Seq[m],{m,1,50}]
Abs[sq]
%O A000001 0
%K A000001 ,nonn,
%A A000001 Roger L. Bagula (tftn@...), Sep 14 2003
RH
RA 209.178.174.68
RU
RI

--
Respectfully, Roger L. Bagula
tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :