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A084834 a(n) is the smallest number not previously used such that a(n)+a(n-1), a(n)+a(n-1)+a(n-2), ..., a(n)+...+a(1) are not prime.

%I A084834 #13 Aug 28 2017 20:17:21
%S A084834 1,3,5,7,9,11,13,15,17,4,6,30,38,10,36,14,34,42,39,21,69,27,33,45,20,
%T A084834 16,24,50,25,51,66,18,72,54,60,74,22,8,19,41,28,48,44,40,78,57,35,58,
%U A084834 102,12,63,65,64,56,46,96,68,76,114,80,52,84,90,99,55,2,93,75,100,62,120,98
%N A084834 a(n) is the smallest number not previously used such that a(n)+a(n-1), a(n)+a(n-1)+a(n-2), ..., a(n)+...+a(1) are not prime.
%C A084834 No sum of a continuous subsequence is ever prime. Is every integer used? Can an odd number ever be surrounded by two even numbers (and similarly for even numbers)?
%H A084834 Chai Wah Wu, <a href="/A084834/b084834.txt">Table of n, a(n) for n = 1..10000</a>
%e A084834 a(4)=7 because 7 is the smallest unused number such that 1+3+5+x, 3+5+x and 5+x are all composite
%o A084834 (PARI) checkprime(a,b)=local(fl); fl=0; for (i=1,b-1,if (isprime(a+s[i]),fl=1; break)); if (fl==0, for (j=1,b-1,if (a==p[j],fl=1; break))); fl
%o A084834 p=vector(300); p[1]=1; pc=2; while (pc<300, x=1; s=vector(300); for (i=1,pc-1,s[i]=sum(k=i,pc-1,p[k])); i=1; while (checkprime(x,pc),x++); p[pc]=x; pc++); p
%Y A084834 Cf. A084833, A254337.
%K A084834 nonn
%O A084834 1,2
%A A084834 _Jon Perry_, Jun 06 2003