A372286 a(n) = number of terms of A086893 that are in the interval [n, A371094(n)].

1, 5, 2, 4, 2, 7, 1, 2, 2, 4, 2, 3, 2, 6, 1, 3, 1, 4, 2, 3, 2, 9, 1, 2, 1, 3, 1, 2, 2, 4, 2, 2, 2, 4, 2, 3, 2, 6, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 8, 1, 2, 1, 3, 1, 3, 1, 5, 1, 3, 1, 3, 1, 3, 1, 6, 1, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 11, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3

Offset

0,2

Comments

a(n) is the number of nonzero terms of A096773 that are found in the interval [n, A371094(n)], inclusive.

Links

Antti Karttunen, Table of n, a(n) for n = 0..21845

Example

A086893 = 1, 3, 5, 13, 21, 53, 85, 213, 341, 853, 1365, 3413, 5461, ...
For n=0, A371094(0) = 1, and only the initial term of A086893 is in the interval [0, 1], therefore a(0) = 1.
For n=1, A371094(1) = 21, so the first five terms of A086893 are in the interval [1, 21], thus a(1) = 5.
For n=6, A371094(6) = 19, and in the interval [6, 19] there is only term 13 of A086893, thus a(6) = 1.
For n=35, A371094(35) = 213, so we count terms 53, 85, 213 of A086893, therefore a(35) = 3.

Prog

(PARI)
A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3); \\ From A086893
A371094(n) = { my(m=1+3*n, e=valuation(m, 2)); ((m*(2^e)) + (((4^e)-1)/3)); };
A372286(n) = { my(u=A371094(n), k1); for(i=1, oo, if(A086893(i)>=n, k1=i-1; break)); for(i=k1, oo, if(A086893(i)>u, return(i-k1-1))); };

Crossrefs

Cf. A086893, A096773, A371094, A372285.

Cf. A002450 (seems to give the positions of records).

Sequence in context: A257480 A181696 A157121 * A368690 A083241 A111145

Adjacent sequences: A372283 A372284 A372285 * A372287 A372288 A372289

Keyword

nonn

Author

Antti Karttunen (proposed by Ali Sada), Apr 28 2024

Status

approved