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Here are the first several entries in a finite sequence of integers.

$$ 31, 45, 71, 89, 91, 94, 111, 112, 118, 121, 126, 131, $$ $$ 134, 135, 139, 143, 144, 145, 148, 158, 161, 189, 193, 194, \dots $$

Your challenge is to identify the sequence, and give its final entry.

________
Let me (again) state for the record that I know What (Not) To Do in a Number Sequence Puzzle. There should be enough information provided here to make this sequence puzzle uniquely solvable.

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2
  • $\begingroup$ You have cleverly avoided alphabetical numerals. $\endgroup$
    – humn
    Mar 17, 2023 at 21:41
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    $\begingroup$ It is a monotone increasing sequence of integers and thus it must converge to infinity! $\endgroup$
    – Yanko
    Mar 18, 2023 at 19:49

1 Answer 1

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The final entry is

2325

Reasoning:

Converting A=1,Z=26 for the first few we get:
CA 31
DE 45
GA 71
HI 89
IA 91
ID 94
These are US state abbreviations, so 111 must be AK.
They are sorted in ascending numerical order, so running all 50 states through this method, the largest and last ends up as WY (Wyoming) = 2325.
(We know it's 50 because DC, Guam, etc. are excluded from the given list.)

An aside:

The 'hint' here (that I didn't notice until I wrote this up) is "let me state"...

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    $\begingroup$ Let me state that this answer is 100% correct. :) $\endgroup$
    – Rubio
    Mar 18, 2023 at 22:21

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