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%I #8 Dec 19 2020 08:00:30
%S 0,0,1,0,1,1,2,0,1,1,2,1,3,2,2,0,3,1,4,1,2,2,5,1,2,3,2,2,6,2,7,0,2,3,
%T 2,1,7,4,3,1,8,2,9,2,2,5,10,1,3,2,4,3,11,2,3,2,5,6,12,2,13,7,3,0,3,2,
%U 13,3,5,2,14,1,15,7,2,4,3,3,16,1,2,8,17,2,4,9,6,2,18,2,4,5,7,10,5,1,19,3,3,2,20,4,21,3,3
%N a(n) = A056239(n) - A000523(n).
%C a(n) is the difference at n between the value of a PrimePi-based pseudo-logarithmic function (A056239) and log_2 floored down (A000523).
%C All terms are nonnegative. (Cf. Bertrand's postulate).
%H Antti Karttunen, <a href="/A339823/b339823.txt">Table of n, a(n) for n = 1..65536</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Bertrand%27s_postulate">Bertrand's postulate</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = A056239(n) - A000523(n).
%o (PARI)
%o A000523(n) = if( n<1, 0, #binary(n) - 1); \\ From A000523
%o A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
%o A339823(n) = A056239(n)-A000523(n);
%Y Cf. A000523, A056239.
%K nonn
%O 1,7
%A _Antti Karttunen_, Dec 18 2020
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