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Omni-MATH / The GEB sequence 1,3,7,12,… is defined by the following properties: (i) the GEB sequence is increasing (that is, each term is larger than the previous term), (ii) the sequence form…

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problem

The GEBGEB sequence 1,3,7,12,…1,3,7,12, \ldots is defined by the following properties: (i) the GEB sequence is increasing (that is, each term is larger than the previous term), (ii) the sequence formed using the differences between each pair of consecutive terms in the GEB sequence (namely, the sequence 2,4,5,…2,4,5, \ldots) is increasing, and (iii) each positive integer that does not occur in the GEB sequence occurs exactly once in the sequence of differences in (ii). What is the 100th term of the GEB sequence?
Plain-text mathematical notation (without MathML)
The GEB sequence 1,3,7,12,… is defined by the following properties: (i) the GEB sequence is increasing (that is, each term is larger than the previous term), (ii) the sequence formed using the differences between each pair of consecutive terms in the GEB sequence (namely, the sequence 2,4,5,…) is increasing, and (iii) each positive integer that does not occur in the GEB sequence occurs exactly once in the sequence of differences in (ii). What is the 100th term of the GEB sequence?
Original LaTeX notation
The $GEB$ sequence $1,3,7,12, \ldots$ is defined by the following properties: (i) the GEB sequence is increasing (that is, each term is larger than the previous term), (ii) the sequence formed using the differences between each pair of consecutive terms in the GEB sequence (namely, the sequence $2,4,5, \ldots$) is increasing, and (iii) each positive integer that does not occur in the GEB sequence occurs exactly once in the sequence of differences in (ii). What is the 100th term of the GEB sequence?

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task_id
669d98cd-6d39-50cb-b38b-1fa996ca0302
task_key
test--669d98cd-6d39-50cb-b38b-1fa996ca0302
task_revision_id
1
config / split
/ test

Official source

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