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%I #4 Jul 17 2018 03:53:16
%S 3,9,12,21,27,30,36,39,48,57,63,66,75,81,84,90,93,102,108,111,117,120,
%T 129,138,144,147,156,165,171,174,183,189,192,198,201,210,219,225,228,
%U 237,243,246,252,255,264,270,273,279,282,291,300,306
%N Numbers of the form (3h+1)*3^(k+1) listed in increasing order.
%C This sequence, call it S and the sequence A016777, call it U, can be defined by mutual induction from the following clauses:
%C a) 1 belongs to U;
%C b) if n belongs to S and m belongs to U then n+m belongs to U;
%C c) if m belongs to U then 3m belongs to S;
%C d) if n belongs to S then 3n belongs to S.
%C A computer-checked proof of this fact is available in the HELM digital library.
%C This sequence appears to contain the numbers whose allegorical signification is connected to the concept of balance according to the Hebrew-Christian-Islamic mystic tradition.
%D F. C. Endres and A. Schimmel, Das Mysterium der Zahl, Eugen Diederichs Verlag, Cologne, 1984 (Italian edition). 1
%H Robert Israel, <a href="/A155504/b155504.txt">Table of n, a(n) for n = 1..10000</a>
%p N:= 1000: # to get terms <= N
%p sort([seq(seq(i*3^j,i=1..floor(N/3^j),3),j=1..floor(log[3](N)))]); # _Robert Israel_, Jul 16 2018
%Y Cf. A016777.
%K nonn
%O 1,1
%A Ferruccio Guidi (fguidi(AT)cs.unibo.it), Jan 23 2009