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Let b(1) = n, b(k+1) = b(k)/2 + k if b(k) is even, b(k+1) = b(k)-k otherwise; sequence gives values of b(1) = n such that b(k) = 2k-4 for k large enough.
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%I #25 Feb 16 2021 10:50:09

%S 1,11,16,18,39,44,53,57,74,102,110,111,116,125,147,152,155,160,201,

%T 218,246,273,287,289,290,292,301,306,323,328,375,380,389,391,396,398,

%U 405,507,512,542,553,570,574,598,625,642,683,688,703,708,715,717,720,729,739,744,746

%N Let b(1) = n, b(k+1) = b(k)/2 + k if b(k) is even, b(k+1) = b(k)-k otherwise; sequence gives values of b(1) = n such that b(k) = 2k-4 for k large enough.

%H Michel Marcus, <a href="/A074197/b074197.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n)/(n*log(n)) seems bounded and maybe a(n) is asymptotic to c*n*log(n) where 3 < c < 5.

%o (PARI) isok(m) = {my(N=1000, v=vector(N), prec=m, nb=0); v[1] = prec; for (n=2, N, v[n] = if (prec % 2, prec-n+1, prec/2+n-1); prec = v[n]; if (prec == 2*n-4, nb++);); nb > N/10;} \\ _Michel Marcus_, Feb 16 2021

%K nonn

%O 1,2

%A _Benoit Cloitre_, Sep 16 2002

%E More terms from _Michel Marcus_, Feb 15 2021