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.

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, 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, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1

Offset: 1

Author

Philip Mizzi, Aug 07 2020

Keywords

• nonn

Comments

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.

Examples

			Start with a(1) = 0.
0 has not occurred before, so the rule says a(2) = 0.
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.
1 has not occurred before, so a(4) = 0.
0 occurred most recently at term a(2) and is not prime, so a(5) = 2.
2 has not occurred before, so a(6) = 0.
0 occurred most recently at term a(4) and is not prime, so a(7) = 2.
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.
.. and so on!
		

Crossrefs

Cf. A181391 (Van Eck's sequence).

Programs

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

Extensions

More terms from Jinyuan Wang, Aug 07 2020