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A336891 Sequence following Van Eck's sequence unless a prime which was previously encountered is found, in which case, a(n+1) = n - m, where m is the largest possible value such that a(m) is also prime.

%I A336891 #35 Sep 13 2020 16:45:10
%S A336891 0,0,1,0,2,0,2,2,1,6,0,5,0,2,2,1,7,0,5,2,1,5,2,1,3,0,8,0,2,4,0,3,3,1,
%T A336891 10,0,5,4,8,12,0,5,5,1,10,10,1,3,5,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,
%U A336891 2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1
%N A336891 Sequence following Van Eck's sequence unless a prime which was previously encountered is found, in which case, a(n+1) = n - m, where m is the largest possible value such that a(m) is also prime.
%C A336891 Van Eck's sequence (A181391) is an integer sequence defined as follows; Let a(0) = 0. For, n >= 0, if there exists an m < n such that a(m) = a(n), take the largest such m and set a(n+1) = n - m, otherwise a(n+1) = 0. This sequence modifies the Van Eck sequence, adding an additional condition in that if a(n) is prime, set a(n+1) = n - m, where m is the largest possible value such that a(m) is also prime.
%e A336891 Start with a(1) = 0.
%e A336891 0 has not occurred before, so the rule says a(2) = 0.
%e A336891 Now 0 HAS occurred before, at a(1), 0 is not prime, so a(3) = 1, which is the number of places before a(2) where 0 occurs.
%e A336891 1 has not occurred before, so a(4) = 0.
%e A336891 0 occurred most recently at term a(2) and is not prime, so a(5) = 2.
%e A336891 2 has not occurred before, so a(6) = 0.
%e A336891 0 occurred most recently at term a(4) and is not prime, so a(7) = 2.
%e A336891 2 occurred most recently at term a(5) and 2 IS prime, so a(8) = 2 which is the number of places back where the previous prime occurred.
%e A336891 .. and so on!
%o A336891 (PARI) lista(nn) = {my(t, v=vector(nn)); for(n=2, nn-1, if(vecsearch(vecsort(v[1..n-1]), v[n]), t=1; if(isprime(v[n]), while(!isprime(v[n-t]), t++), while(v[n-t]!=v[n], t++)); v[n+1]=t)); v; } \\ _Jinyuan Wang_, Aug 20 2020
%Y A336891 Cf. A181391 (Van Eck's sequence).
%K A336891 nonn
%O A336891 1,5
%A A336891 _Philip Mizzi_, Aug 07 2020
%E A336891 More terms from _Jinyuan Wang_, Aug 07 2020