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A254341 Lexicographically earliest sequence of distinct numbers with alternating parity such that no sum of consecutive terms is prime.

%I A254341 #20 Jan 29 2015 21:32:24
%S A254341 0,1,8,25,24,27,6,9,30,15,42,39,18,21,36,33,60,35,16,69,48,63,12,51,
%T A254341 66,45,72,87,54,93,78,81,90,57,84,75,114,111,96,99,120,105,102,117,
%U A254341 144,123,108,129,126,135,138,147,150,141,162,153,156,159,132,171,174,165,168,177,192,183,180,189,186,195,198,207,204,201,216,213,228,219,210,231,222,249,240,237,252,243,258,255,234,261,246,225,288,267,264,273,276,279,270
%N A254341 Lexicographically earliest sequence of distinct numbers with alternating parity such that no sum of consecutive terms is prime.
%C A254341 In other words, no sum a(i)+a(i+1)+a(i+2)+...+a(j) may be prime. In particular, the sequence may not contain any primes.
%C A254341 Without the condition that the parity alternates, it seems that the sequence (A254337) contains only a single odd number.
%C A254341 It appears that a(n) ~ 3n. Is there a simple explanation for this?
%H A254341 M. F. Hasler, <a href="/A254341/b254341.txt">Table of n, a(n) for n = 0..9999</a>
%o A254341 (PARI) {N=10^3; a=[]; u=0; for(i=0,N, a=concat(a,i%2); until( ! isprime(s) || ! a[#a]+=2, while( isprime(a[#a]) || bittest(u,a[#a]), a[#a]+=2);  s=a[k=#a]; while( k>1 && ! isprime( s+=a[k--]),)); u+=2^a[#a])}
%Y A254341 Cf. A254337, A153136.
%K A254341 nonn
%O A254341 0,3
%A A254341 _M. F. Hasler_, Jan 29 2015