OEIS format for base b representation of constants

The current format for storing the base

b, b > 1,

expansion of a constant

C

is the following:

• If the sequence gives the base

  b

  expansion of a constant, the offset is the number of digits in base

  b

  before the base

  b

  fractional point.

     

offset  =  ⎰   ⎱     0  if | C | < 1, 1 + ⌊  logb | C | ⌋  if | C | ≥ 1.

e.g.:

• for A062964 Hexadecimal expansion of

  π

  . (3.243...)16 (offset is 1)
• for A004608 Base 9 expansion of

  π

  . (3.124...)9 (offset is 1)
• for A129406 Base 3 expansion of

  L (3, χ3 )

  , where

  L (3, χ3 )

  is the Dirichlet

  L

  -function for the non-principal character modulo 3. (0.212212...)3 (offset is 0)
• for A014578 Binary expansion of Thue constant (Roth’s constant). (0.011011...)2 (offset is 0)

• Thus

| C |  =  b offset  − 1   ∞ ∑   m  = 0    an = m + offset b  − m.

Examples

• Search OEIS for keyword “cons”

See also

• OEIS format for decimal representation of constants
• Explanation of terms used in reply from, section “offset”
• User:Charles R Greathouse IV/Format
• Internal OEIS format