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

1,5

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.

Links

Table of n, a(n) for n=1..86.

Example

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!

Prog

(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

Crossrefs

Cf. A181391 (Van Eck's sequence).

Sequence in context: A112803 A124242 A112274 * A181391 A333359 A350151

Adjacent sequences: A336888 A336889 A336890 * A336892 A336893 A336894

Keyword

nonn

Author

Philip Mizzi, Aug 07 2020

Extensions

More terms from Jinyuan Wang, Aug 07 2020

Status

approved