A335155 -id:A335155 - cp's OEIS frontend

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

Rémy Sigrist, Jun 06 2020

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.

			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

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A335409

Cf. A335155, A335365, A335393.

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

A335393 a(1) = 1 and for any n >= 1, a(2n) = a(n) + 5, a(2n+1) = a(n) * 3.

Original entry on oeis.org

1, 6, 3, 11, 18, 8, 9, 16, 33, 23, 54, 13, 24, 14, 27, 21, 48, 38, 99, 28, 69, 59, 162, 18, 39, 29, 72, 19, 42, 32, 81, 26, 63, 53, 144, 43, 114, 104, 297, 33, 84, 74, 207, 64, 177, 167, 486, 23, 54, 44, 117, 34, 87, 77, 216, 24, 57, 47, 126, 37, 96, 86, 243

Offset: 1

Rémy Sigrist, Jun 05 2020

nonn

All terms belong to A335155.

For any k > 0, the value k appears A335392(k) times.

			a(12) = a(6) + 5 = a(3) + 5 + 5 = a(1) * 3 + 5 + 5 = 1 * 3 + 5 + 5 = 13.

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Cf. A335155, A335365, A335392.

a(n) = { if (n==1, 1, n%2==0, a(n\2)+5, a(n\2)*3) }

a(2^k) = 1 + 5*k for any k >= 0.

a(2^k-1) = 2^(k-1) for any k > 0.

cp's OEIS Frontend

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

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A335393 a(1) = 1 and for any n >= 1, a(2n) = a(n) + 5, a(2n+1) = a(n) * 3.

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cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A335393 a(1) = 1 and for any n >= 1, a(2*n) = a(n) + 5, a(2*n+1) = a(n) * 3.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A335393 a(1) = 1 and for any n >= 1, a(2n) = a(n) + 5, a(2n+1) = a(n) * 3.