OEIS format for decimal representation of constants

The value of the constant 

C

encoded as a sequence of decimal digits is:

$|C|=10^{{\rm {offset}}-1}\cdot \sum _{m=0}^{\infty }a_{n=m+{\rm {offset}}}\,10^{-m}\,$

Generally, the offset is the number of digits before the decimal point:

${\rm {offset}}={\begin{cases}0&{\text{if }}|C|<1,\\{\lfloor \log _{10}(|C|)\rfloor +1}&{\text{if }}|C|\geq 1.\end{cases}}\,$

e.g.:

• for Pi = 3.14159... it is offset = 1,
• for gamma = 0.5772... it is offset = 0,
• for sin(1°) = 0.01745... it is also offset = 0,
• for alpha = 0.007297... it is again offset = 0 and
• for 1/alpha = 137.0359... it is offset = 3.

But if the number of initial zeros would be too large to reasonably include, it can be encoded as a negative offset, as A143531, which has offset −14827:

1, 8, 2, 8, 6, 4, 3, 2, ...

$1.828\ldots \cdot 10^{-14828}=10^{-14827-1}\left(1\cdot 10^{0}+8\cdot 10^{-1}+2\cdot 10^{-2}+\cdots \right)$

If the number of initial zeros is too large (in absolute value) to be recorded as the offset at all, like A160106, give the offset as 1 and record the proper offset (if possible) as a comment.

Uncertainty

If a constant is known only with some uncertainty, only the digits that are valid within the whole confidence interval (typically plus-minus standard deviation) should be included. Example: according to CODATA 2022, muon-electron mass ratio A057720 equals 206.7682827(46), so only digits 2067682 should be included in the sequence entry.

Examples

• Search OEIS for keyword "cons"

• Cf. Talk:OEIS format for decimal representation of constants#Offset for the following:

16.789 has offset 2 1.67 has offset 1 .678 has offset 0 .0678 has offset -1 .00678 has offset -2

According to these above examples, we could have

• for sin(1°) = 0.01745... offset = –1 instead of offset = 0,
• for alpha = 0.007297... offset = –2 instead of offset = 0,

but we don't because the initial 0's are included in those sequences.

See also

• OEIS format for base b representation of constants
• Explanation of Terms Used in Reply From, section "Offset"
• User:Charles R Greathouse IV/Format
• Internal Format Used In The OEIS