A335409 a(n) is the least k such that A335155(n) = A335393(k).

1, 3, 2, 6, 7, 4, 12, 14, 8, 5, 28, 16, 10, 13, 32, 15, 20, 26, 64, 30, 9, 52, 128, 60, 18, 25, 256, 29, 36, 50, 512, 58, 17, 100, 1024, 116, 34, 11, 2048, 57, 68, 22, 4096, 114, 33, 44, 8192, 228, 66, 21, 16384, 27, 132, 42, 32768, 54, 65, 84, 31, 108, 130

Offset

1,2

Comments

For any n > 0, the binary representation of a(n) encodes a minimal way (in the sense of the number of operations) of obtaining A335155(n) by starting from 1 and then repeatedly adding 5 or multiplying by 3; the leading 1 corresponds to the starting value 1, and then the 0's correspond to adding 5 and the 1's correspond to multiplying by 3.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A335409

Formula

A335155(n) = A335393(a(n)).

Example

The first terms, alongside their binary representation and A335155(n), are:
  n   a(n)  bin(a(n))  A335155(n)
  --  ----  ---------  ----------
   1     1          1   1 = 1
   2     3         11   3 = 1*3
   3     2         10   6 = 1+5
   4     6        110   8 = (1*3)+5
   5     7        111   9 = 1*3*3
   6     4        100  11 = 1+5+5
   7    12       1100  13 = (1*3)+5+5
   8    14       1110  14 = (1*3*3)+5
   9     8       1000  16 = 1+5+5+5
  10     5        101  18 = (1+5)*3
  11    28      11100  19 = (1*3*3)+5+5
  12    16      10000  21 = 1+5+5+5+5

Prog

(PARI) See Links section.

Crossrefs

Cf. A335155, A335365, A335393.

Sequence in context: A083362 A182847 A182869 * A236341 A293835 A258145

Adjacent sequences: A335406 A335407 A335408 * A335410 A335411 A335412

Keyword

nonn,base

Author

Rémy Sigrist, Jun 06 2020

Status

approved