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Offsets
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The offset in an OEIS sequence entry gives the index of the first term of the sequence (in other words, it tells us where the sequence starts). Given a sequence of a function 
with offset 3, this tells us that the first listed corresponds to 
. Below are some examples.
Contents |
Examples of offsets
Offset 0
- Functions that are defined for all integers, and more pointedly, are a mapping from the integers to the integers. For example,
. Theoretically, we could start our listing at –3 or –7, but these are rather arbitrary choices, and the choice of 
doesn't give a well-ordered (i.e. no first term) sequence. Therefore, the logical offset is 0 (indeed that is the offset of A000290). In any case, for this example, since 
, this presents no loss of information (otherwise, there may be two separate sequences, one for 
and the other for .
- Functions that are defined for all nonnegative integers. For example,
(see A000196).[1]
- Decimal expansion of constants that are in the interval [0.1, 1). For example, the decimal expansion of the Euler-Mascheroni constant, A001620. See OEIS format for decimal representation of constants for a more in-depth discussion of the offset of decimal expansions.
Offset 1
- Lists should should be 1-indexed (rather than 0-indexed). For example, in Leporello's famous "catalogue aria" from Don Giovanni, he sings five numbers, "seicento e quaranta," "duecento e trentuna," "cento," "novantuna," "mille e tre."[2] So, 640 is the first number he sings, and therefore, the offset of A027885 is 1.
Offset 2
- A112823 Largest prime
in any decomposition of 
into a sum of two primes. If a smaller value was chosen, not all values would be defined.
Offset 3
- A002374 Largest prime in any decomposition of into a sum of two odd primes. If a smaller value was chosen, not all values would be defined.
Notes
- ↑ Of course for negative integers, we need only multiply the values of this sequence by the imaginary unit, assuming we understand the definition as being
, and that 
returns a real value that the floor function can then handle ordinarily. - ↑ Aaron Greene, Leporello's "Catalog Aria" from Mozart's opera Don Giovanni: Lyrics and English Translation About.com
