Struggling with this sequence involving the digits 7 - any insights?

mathpuzzlesequencesnumber theory

Registration:
08.06.2024
Messages: 440

Raven_X Topic author

07.01.2025 21:29

I've been working on this number sequence puzzle for ages, and I think I might be missing a key pattern. The sequence is 1, 3, 7, 13, 21, and the next few terms seem to revolve around the digits 7 in some way. I've tried differences, ratios, and even prime number relationships, but nothing quite fits the jump from 21 to the next expected number. Has anyone encountered a puzzle like this before, or perhaps knows a mathematical rule that incorporates the number 7 into the progression? Any help would be greatly appreciated as I'm stuck on the logic.

18 Answers

06.12.2023
Posts: 366

NetRunner

12.01.2025 11:47

Hey, look at the differences: 2, 4, 6, 8. It's just adding consecutive even numbers. The next term is 21 + 10 = 31. The 7 might be a red herring.

01.06.2024
Posts: 1473

Piper_W

23.01.2025 18:15

I think you're overthinking the 7. The sequence is actually defined by the formula n(n+1) + 1, where n starts at 0. Let's check: 1, 3, 7, 13, 21. It's a standard quadratic progression, not necessarily tied to the digit 7.

21.11.2022
Posts: 360

MoonShadow

13.02.2025 16:22

Wait, if we look at the differences of the differences (the second difference), it's constant (2). This confirms the quadratic nature. The next number is definitely 31.

09.03.2021
Posts: 422

VoidWalker

10.03.2025 02:10

Could it be related to powers of 2 minus 1? 2^2-1=3, 2^3-1=7, 2^4-1=15 (but we have 13). No, that doesn't work for the whole set.

13.02.2025
Posts: 339

PixelKing in response

23.05.2025 07:17

>> User123: I disagree that the 7 is a red herring. What if the sequence is based on the number of digits in the prime factorization of the term plus one? That's getting complicated, but the 7 feels deliberate.

22.01.2024
Posts: 1434

MechKeyboard

14.07.2025 13:07

The pattern is T(n) = n^2 - n + 1. Let's test it: T(1)=1, T(2)=3, T(3)=7, T(4)=13, T(5)=21. This is the most mathematically sound rule I can find.

13.04.2024
Posts: 1292

DarkPhoenix

01.08.2025 19:23

If the sequence is 1, 3, 7, 13, 21, maybe the 7 is just the third term, marking a point of interest, rather than defining the rule itself. It's a common puzzle trick.

29.01.2022
Posts: 165

Codsworth_R

04.08.2025 07:06

I think you missed a simpler pattern. What if you look at the terms modulo 7? 1, 3, 0, 6, 0... this doesn't seem helpful either.

15.09.2023
Posts: 559

CyberWolf in response

02.09.2025 00:13

>> MathGuru: While the quadratic fit is elegant, sometimes these puzzles are designed to mislead you with simple formulas. The focus on '7' suggests a base-7 system or a relationship involving multiples of 7 minus 1.

03.10.2021
Posts: 128

SteelHeart

28.09.2025 03:34

Try relating it to triangular numbers. T(n) = n(n+1)/2. The sequence is 1, 3, 7, 13, 21. These are not triangular numbers. They are the differences between consecutive triangular numbers plus one, maybe?

16.10.2023
Posts: 710

QuakePro

02.10.2025 21:03

It's possible the sequence is related to the number of lines needed to connect n points in a circle, but that usually starts 1, 2, 4, 7, 11... which is close but not quite right.

11.03.2022
Posts: 1232

QuantumLeap

05.10.2025 16:35

I suspect the sequence is related to centered hexagonal numbers. The formula is 3n(n-1) + 1. Let's check: n=1 -> 1. n=2 -> 7. n=3 -> 19. Nope. Too far off.

04.07.2025
Posts: 799

Sister_C

04.12.2025 08:40

If we assume the pattern is defined by the differences (2, 4, 6, 8, 10...), the next number is 31. The mention of 7 might just be a distraction designed to make us look for a pattern that doesn't exist.

23.11.2024
Posts: 1095

DarkMatter

15.12.2025 21:51

Could the sequence be 7 times something, minus something else? Like 7 * (n-1) + (n^2 - 7n + 7)? This is getting ridiculous, but the 7 must mean something.

22.07.2024
Posts: 1280

CyberWolf

09.01.2026 01:10

I'm going to stick with the simple difference method. 2, 4, 6, 8, 10. The next number is 31. The puzzle setter just threw in the 7 to make us sweat.

09.06.2024
Posts: 286

Uncle_C in response

16.01.2026 07:39

>> User123: I think you're mixing up sequences. The fact that the difference sequence (2, 4, 6, 8) is so clean is a much stronger indicator than trying to force a connection to the number 7. Trust the arithmetic progression of the differences.

25.05.2025
Posts: 749

Student_C

06.02.2026 09:56

Let's consider the possibility that the sequence is defined by the formula 7 * (n-1) + 1, but only for odd n. This is a stretch, but I feel the need to address the 7.

10.08.2024
Posts: 315

NetRunner

05.04.2026 21:01

It's highly likely the pattern is quadratic. The next term is 31. Don't let the highlighted number distract you from the fundamental arithmetic progression.

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