THE COLLATZ CONJECTURE

halve the even, triple the odd and add one: the road of 27, the record holders and a problem nobody has solved

Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.

Three sizes in one archive — from a sheet on the fridge to a poster on the wall.

Formats: A4 · A3 · A2
What you get: Print-ready PDFs, one per size, with every letterform converted to outlines — nothing to install, nothing to shift.
Subject: maths · everyone · reference · study

A step here means one operation: both the halving and the tripling-and-adding-one. The heights of the bars are the values themselves, with no scale compression. The conjecture is unproven: every number up to 2⁶⁸ has been checked by machine (D. Barina, “Convergence verification of the Collatz problem”, The Journal of Supercomputing, 2020), but a check is not a proof.

NEIGHBOURING NUMBERS TAKE COMPLETELY DIFFERENT ROADS

Neighbouring numbers have nothing in common. 26 reaches one in 10 steps and 28 in 18, while 27, sitting between them, climbs to 9 232 — more than 340 times its own size — and takes 111 steps.

That peak of 9 232 is not its own: of the 999 numbers below a thousand, exactly 353 rise to it and no higher. Every one of them passes through the same point and falls back down the same road — more than a third of all starting points sooner or later become one and the same journey.

On the sheet

A step here means one operation: both the halving and the tripling-and-adding-one. The heights of the bars are the values themselves, with no scale compression. The conjecture is unproven: every number up to 2⁶⁸ has been checked by machine (D. Barina, “Convergence verification of the Collatz problem”, The Journal of Supercomputing, 2020), but a check is not a proof.
Colour carries meaning, but meaning never rests on colour alone — the sheet reads in black and white.
Nothing about how it was made: the sheet carries only what the reader needs.

Printing

Three sizes in the archive: A4 — 210×297 mm, A3 — 297×420 mm, A2 — 420×594 mm.
All text is converted to outlines. No fonts to install, and nothing shifts on another machine.
White background and sparing fills — it prints on a home printer without draining the cartridge.
Margins of at least 10 mm: a home printer cannot print to the edge.
No stroke thinner than 0.3 mm, so nothing disappears in print.

Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 11 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.

THE COLLATZ CONJECTURE

NEIGHBOURING NUMBERS TAKE COMPLETELY DIFFERENT ROADS

On the sheet

Printing

More like this

BARBELL MATHS

BENFORD’S LAW

THE BIRTHDAY PARADOX

THE CLOCK FACE