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 A155504 Numbers of the form (3h+1)*3^(k+1) listed in increasing order. 1
 3, 9, 12, 21, 27, 30, 36, 39, 48, 57, 63, 66, 75, 81, 84, 90, 93, 102, 108, 111, 117, 120, 129, 138, 144, 147, 156, 165, 171, 174, 183, 189, 192, 198, 201, 210, 219, 225, 228, 237, 243, 246, 252, 255, 264, 270, 273, 279, 282, 291, 300, 306 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence, call it S and the sequence A016777, call it U, can be defined by mutual induction from the following clauses: a) 1 belongs to U; b) if n belongs to S and m belongs to U then n+m belongs to U; c) if m belongs to U then 3m belongs to S; d) if n belongs to S then 3n belongs to S. A computer-checked proof of this fact is available in the HELM digital library. 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. REFERENCES F. C. Endres and A. Schimmel, Das Mysterium der Zahl, Eugen Diederichs Verlag, Cologne, 1984 (Italian edition). 1 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 MAPLE N:= 1000: # to get terms <= N sort([seq(seq(i*3^j, i=1..floor(N/3^j), 3), j=1..floor(log[3](N)))]); # Robert Israel, Jul 16 2018 CROSSREFS Cf. A016777. Sequence in context: A310323 A212059 A226152 * A270672 A211217 A307201 Adjacent sequences: A155501 A155502 A155503 * A155505 A155506 A155507 KEYWORD nonn AUTHOR Ferruccio Guidi (fguidi(AT)cs.unibo.it), Jan 23 2009 STATUS approved

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Last modified February 29 00:26 EST 2024. Contains 370400 sequences. (Running on oeis4.)