A155504 Numbers of the form (3h+1)*3^(k+1) listed in increasing order.

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

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