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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
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
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.)