Brain Teaser: What Do These Sequences Have in Common?

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Discussion Overview

The discussion revolves around identifying commonalities among various numerical sequences presented as a brain teaser. Participants explore potential patterns, mathematical relationships, and characteristics of the sequences, which include arithmetic progressions and other numerical properties.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • Some participants suggest that all sequences are simple sequences defined by specific recursive relationships.
  • Others propose that all numbers in the sequences are integers and point out that concatenating the digits reveals the digits "201" in each sequence.
  • It is noted that each sequence's odd-numbered entries are odd.
  • A claim is made that adding the 25th through 35th digits of the concatenated sequences yields the same total, 42.
  • One participant questions the relevance of the number 7 to the third sequence, indicating uncertainty about its applicability.
  • Another participant expresses frustration, suggesting that the criteria have been met and is seeking validation or a better answer.

Areas of Agreement / Disagreement

Participants express differing views on the commonalities of the sequences, with no consensus reached on a singular answer. Multiple competing interpretations of the sequences' characteristics remain present.

Contextual Notes

Some claims depend on specific interpretations of the sequences and the definitions of terms like "simple sequences." The discussion includes unresolved aspects regarding the significance of certain numbers and properties.

Who May Find This Useful

Individuals interested in mathematical puzzles, sequence analysis, or brain teasers may find this discussion relevant.

math_04
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1,8,15,22,29,36,...

49,343,2401,....

77,74,71,68,65,....

What do all these sequences have in common?
 
Mathematics news on Phys.org
The digit 1
:smile:
 
Well, they're all simple sequences...

n=(n-1)+7
n=(n-1)x7
n=(n-1)-3
 
- All of the numbers in the sequences are integers.
- If you concatenate the digits of the sequences, each one has the digits "201".
- Each sequence's odd-numbered entries are odd.
- If you concatenate the digits of each sequence, and add the 25th through 35th digits, you'll get the same total, 42.

DaveE
 
The number 7?
 
sigh.

Commas, ellipses and integers.

Asked & answered.

math_04: we've given answers that have met the criteria. Either grant us a win or tell us there's a better answer than the ones we've provided.
 
I guess its the number seven and the digits being integers. Am I getting the right answer to the teasers?





------------------
tease your eyes
 
I don't see what 7 has to do with the third sequence.
 

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