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%I #15 Apr 28 2024 16:29:11
%S 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,
%T 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,
%U 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
%N a(n) = number of terms of A086893 that are in the interval [n, A371094(n)].
%C a(n) is the number of nonzero terms of A096773 that are found in the interval [n, A371094(n)], inclusive.
%H Antti Karttunen, <a href="/A372286/b372286.txt">Table of n, a(n) for n = 0..21845</a>
%e A086893 = 1, 3, 5, 13, 21, 53, 85, 213, 341, 853, 1365, 3413, 5461, ...
%e For n=0, A371094(0) = 1, and only the initial term of A086893 is in the interval [0, 1], therefore a(0) = 1.
%e For n=1, A371094(1) = 21, so the first five terms of A086893 are in the interval [1, 21], thus a(1) = 5.
%e For n=6, A371094(6) = 19, and in the interval [6, 19] there is only term 13 of A086893, thus a(6) = 1.
%e For n=35, A371094(35) = 213, so we count terms 53, 85, 213 of A086893, therefore a(35) = 3.
%o (PARI)
%o A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3); \\ From A086893
%o A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
%o 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))); };
%Y Cf. A086893, A096773, A371094, A372285.
%Y Cf. A002450 (seems to give the positions of records).
%K nonn
%O 0,2
%A _Antti Karttunen_ (proposed by _Ali Sada_), Apr 28 2024
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