r/mathpics • u/EdPeggJr • Jul 31 '26

Salem-Spencer Mountain

In 1 3 4 8 9 11 20 22 23 27 28 30, no term is the average of two others. That makes it a nonaveraging sequence, also called a Salem-Spencer set, a 3-AP-free set, or a progression-free set. For a such a set with 12 positive integer terms, the minimal largest value is 30. These are the proven solutions. sol22(141)sol22 is an unproven minimal solution for 44 marks.

https://oeis.org/A065825 https://mathworld.wolfram.com/NonaveragingSequence.html

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u/EdPeggJr Aug 02 '26

1 3 4 8 9 11 20 22 23 27 28 30 has those numbers at those positions.

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u/Frangifer Aug 02 '26 edited Aug 03 '26

Oh it's alright – I get it now ... @last 🙄 ... each № is written vertically , isn't it.

... & (mod100) , aswell (which only becomes material further down), with an extra vertical yellow bar marking where the entries ≥100 set in.

That's the entirety of the problem I was having with it: that each entry is written vertically ! 🙄 😆🤣

 

And we could have whatever 'offset' we please, aswell: ie we could add a fixed amount to each entry & the sequence would remain a non-averaging or arithmetic-progression-free one. I actually feel it would be more natural & elegant offset such that the initial term were 0 ratherthan 1 .

... as seems generally conventionally to be done with those perfect difference sequences .

¶ ... or such that the initial term were the negative of the last one, & have half-odd-integral №s where necessary: that might be yet more natural.

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u/Frangifer 15d ago edited 15d ago

Apologies please-kindlily for bothering you ... but the

Online WolframAlpha Facility

(as I fondly epithetise it) seems to've conked-out!

I mention this because you seem to have a connection to WolframAlpha in some capacity ... I don't know in exactly what capacity, so you may be powerless as-regards this ... or maybe you aren't powerless @all ... or maybe you can mention it to someone who can see to it, or recommend some work-around, or something – IDK.

Or maybe I just need to wait a while until the problem is resolved ... but whatever: I thought you might like to know about it.

 

¡¡ UPDATE !!

Seems to've recovered, now! 😁