A053789 Smallest prime divisor of sum of first k primes for nonprime k (?)

[zak seidov]

Something wrong is here:

if 1,4,6,8 are first four nonprime k's,
then sums are 2, 17, 41, 77 
and spd's are 2,7,41,7
not 2,2,2,7,
right?

i guess that not k but sum'd be nonprime;
if so then first nonprime sums are
10, 28, 58, 77
with correct spd's 
2,2,2,7,
right?
zak

if so i suggest corrected %N as this:

%N A053789 Smallest prime divisor of sum s of first k
primes for nonprime s.

******** as in OEIS at present *************
%S A053789
2,2,2,7,2,3,2,2,2,3,2,3,2,3,2,7,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,41,2,3,

%N A053789 Smallest prime divisor of sum  of first k
primes for nonprime k.

Enoch Haga (Enokh(AT)comcast.net)



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zs> From seqfan-owner at ext.jussieu.fr  Mon Feb 25 20:26:00 2008
zs> Date: Mon, 25 Feb 2008 11:24:41 -0800 (PST)
zs> From: zak seidov <zakseidov at yahoo.com>
zs> Subject: A053789 Smallest prime divisor of sum of first k primes for nonprime k (?)
zs> To: njas at research.att.com, Enokh at comcast.net, seqfan at ext.jussieu.fr
zs> 
zs> Something wrong is here:
zs> 
zs> if 1,4,6,8 are first four nonprime k's,
zs> then sums are 2, 17, 41, 77 
zs> and spd's are 2,7,41,7
zs> not 2,2,2,7,
zs> right?
zs> 
zs> i guess that not k but sum'd be nonprime;
zs> if so then first nonprime sums are
zs> 10, 28, 58, 77
zs> with correct spd's 
zs> 2,2,2,7,
zs> right?
zs> zak
zs> 
zs> if so i suggest corrected %N as this:
zs> 
zs> %N A053789 Smallest prime divisor of sum s of first k
zs> primes for nonprime s.
zs> 
zs> ******** as in OEIS at present *************
zs> %S A053789
zs> 2,2,2,7,2,3,2,2,2,3,2,3,2,3,2,7,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,41,2,3,
zs> 
zs> %N A053789 Smallest prime divisor of sum  of first k
zs> primes for nonprime k.
zs> 
zs> Enoch Haga (Enokh(AT)comcast.net)

What was meant is a definition: "Smallest prime divisor of n-th composite 
partial sum of primes"
or easier:
A053789(n)= A020639(A053790(n))

Maple hack which prints A053789 thus defined follows
RJM
----------------------------------------------------

A007504 := proc(n) option remember ;
end:
isA007504 := proc(n)
end:
isA053790 := proc(n)
end:
A053790 := proc(n) option remember ;
end:
A020639 := proc(n)
end:
A053789 := proc(n)
end:

for n from 1 to 50 do
od;




If we read the Catalan numbers A000108 modulo 4, we apparently get
which seems to be the content of Theorem 2.3 of
Eu-Liu-Yeh's
<a href="http://www.math.sinica.edu.tw/mathuser/file_upload/mayeh/MotzkinMod_f.pdf">Catalan and Motzkin numbers modulo 4 and 8</a> .

Could s.o. with a higher mathematical background confirm this and perhaps
yet to appear in the OEIS.

Richard J. Mathar
------
Maplish:
A000108 := proc(n)
end:

A001006 := proc(n)
end:

# Motzkin's modulo 8
a := proc(n)
end:

for n from 0 to 80 do
od: