%I #26 Jan 21 2023 19:43:28
%S 1,8,1,15,9,1,14,6,30,6,9,15,6,4,8,12,10,14,6,12,8,10,12,18,12,6,6,6,
%T 24,6,6,8,1,9,6,10,8,12,6,14,10,6,4,8,12,10,20,6,18,6,6,4,8,12,6,4,12,
%U 8,10,8,6,6,18,6,6,20,10,12,8,4,6,12,12,6,12,6,12
%N Lexicographically earliest sequence of positive numbers in which no set of consecutive terms sums to a prime.
%C Terms >= 30 seem to be very rare. Up to a(450000), 30 appears only 7 times: at n = 9, 288, 2507, 15902, 54405, 242728, 425707.
%C For n <= 450000, the largest term is 32; it appears at n = 335308 and 370687.
%H Alois P. Heinz, <a href="/A332941/b332941.txt">Table of n, a(n) for n = 1..10000</a>
%p s:= proc(i, j) option remember; `if`(i>j, 0, a(j)+s(i, j-1)) end:
%p a:= proc(n) option remember; local k; for k while
%p ormap(isprime, [k+s(i, n-1)$i=1..n]) do od; k
%p end:
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Mar 23 2020
%t s[i_, j_] := s[i, j] = If[i > j, 0, a[j] + s[i, j-1]];
%t a[n_] := a[n] = Module[{k}, For[k = 1, AnyTrue[k+Table[s[i, n-1], {i, 1, n}], PrimeQ], k++]; k];
%t Array[a, 100] (* _Jean-François Alcover_, Nov 17 2020, after _Alois P. Heinz_ *)
%o (Python)
%o def A(ee):
%o a=[1]
%o print(1)
%o n=1
%o while n<=ee:
%o i=1
%o while i>0:
%o ii=i
%o iz=c=0
%o while iz<=len(a):
%o c=0
%o if ii>2:
%o for j in range(2, int((ii)**0.5+1.5)):
%o if ii%j==0:
%o c=1
%o break
%o if c==0 and ii>1:
%o break
%o else:
%o iz += 1
%o ii=ii+a[n-iz]
%o if c==1:
%o n += 1
%o a.append(i)
%o print(i)
%o break
%o if i<4:
%o i=4
%o else:
%o i += 1
%o return a
%Y Cf. A254337, A084833.
%K nonn
%O 1,2
%A _S. Brunner_, Mar 03 2020