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a(0) = 0; for n>0, a(n) is the index of the last term in A109812 that is <= 2^n - 1.
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%I #17 Apr 26 2022 03:37:38

%S 0,1,4,16,28,76,162,418,650,1892,3555,7252,20059,39786,84653,174566,

%T 343911,690189,1688099,3366971,7131089,14446268,31036955,62485240,

%U 145444358,290692248,624275567

%N a(0) = 0; for n>0, a(n) is the index of the last term in A109812 that is <= 2^n - 1.

%C It appears that the last term in A109812 of binary length n is always 2^n - 1 itself. The term after that is (by definition) A352206(n).

%C If we subtract 1 from a(n), we appear to get a subsequence of A352204, the indices of record high points in A109812.

%C There are also occasional near-coincidences with A305370.

%e The last term in A109812 of binary length at most 3 is A109812(16) = 7, so a(3) = 16.

%Y Cf. A109812, A305370, A352203, A352204, A352206.

%K nonn,base,more

%O 0,3

%A _N. J. A. Sloane_ and _Chai Wah Wu_, Mar 29 2022

%E a(18)-a(26) from _Walter Trump_, Apr 26 2022