

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
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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 computerchecked 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 HebrewChristianIslamic 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



KEYWORD

nonn


AUTHOR

Ferruccio Guidi (fguidi(AT)cs.unibo.it), Jan 23 2009


STATUS

approved



