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

[Richard Mathar]

submit this as a comment to A073267 ? The Motzkin's modulo 8 seem not
  
	binomial(2*n,n)/(n+1) ;
        add( binomial(n,2*k)*A000108(k),k=0..n/2) ;
        A001006(n) mod 8 ;
	# print(n,A000108(n),A000108(n) mod 4) ;
	printf("%d,",A000108(n) mod 4) ;
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Date: Mon, 25 Feb 2008 19:26:25 -0800 (PST)
From: zak seidov <zakseidov at yahoo.com>
Subject: Number of positive solutions of the Diophantine x*p+y*q=(p+q)^3, 
To: seqfan at ext.jussieu.fr, njas at research.att.com
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Dear seqfans,
is it 
new/correct/interesting/nice,
or
old/wrong/dumb?
thanks, zak

%I A000001
%S A000001
21,34,49,76,97,122,145,169,211,241,274,313,337,361,401,449,481,513,553,577,609,649,689,745,793,817,841,865,889,963,1033,1073,1105,1153,1201,1233,1281,1321,1361,1409,1441,1489,1537,1561,1585,1641,1737,1801,1825,1849,1889,1921,1969,2033,2081,2129,2161,2193,2233,2257,2305,2401,2473,2497,2521,2593,2673,2737,2785,2809,2849,2905,2961,3009,3049,3089,3145,3193,3241,3313,3361,3409,3457,3489,3529,3569,3625,3673,3697,3721,3785,3865,3913,3961,4009,4049,4121,4177,4257,4353
%N A000001 Number of positive solutions of the
Diophantine x*p+y*q=(p+q)^3, p=n-th prime, q=(n+1)-th
prime.
%e A000001 a(1)=21 because Diophantine 2x+3y=(2+3)^3
has 21 positive solutions {x,y}:
{1,41},{4,39},{7,37},{10,35},{13,33},{16,31},{19,29},{22,27},{25,25},{28,23},{31,21},{34,19},{37,17},{40,15},{43,13},{46,11},{49,9},{52,7},{55,5},{58,3},{61,1};
a(2)=34 because Diophantine 3x+5y=(3+5)^3 has 34
positive solutions {x,y}:
{4,100},{9,97},{14,94},{19,91},{24,88},{29,85},{34,82},{39,79},{44,76},{49,73},{54,70},{59,67},{64,64},{69,61},{74,58},{79,55},{84,52},{89,49},{94,46},{99,43},{104,40},{109,37},{114,34},{119,31},{124,28},{129,25},{134,22},{139,19},{144,16},{149,13},{154,10},{159,7},{164,4},{169,1}.
%t A000001
Table[With[{p=Prime[n],q=Prime[n+1]},Floor[(p+q)^2/p]+Floor[(p+q)^2/q]+1],{n,1,100}]
%O A000001 1
%K A000001 ,nonn,
%A A000001 Zak Seidov (zakseidov(AT)yahoo.com), Feb 25
2008



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