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Read this story online a few years back but I am quite sure it was far older, maybe from the 1970s or even earlier.

It has a pair of scientists receiving a transmission from a distant star system. Initially they have trouble deciphering the message, but then they realize it's chemical formulae rather than language or mathematics. They realize that the distant aliens are telling the story of their history in terms of chemistry - the first formula describes the combustion of plant matter (ie the invention of fire) then come formulae about iron making, coal burning, etc. The next sequence of formulae are decoded and turn out to be stuff like gunpowder and eventually nuclear fission, which is repeated over and over which the scientists decide must mean multiple nuclear wars. Finally a set of increasingly complicated formulae are received that our scientists don't recognize, ending in a single formula that they sense must be for something really destructive. Not long afterwards, the distant star explodes. The scientists speculate that the distant aliens who sent the transmission were scientists as well, who knew that their star was about to die and wanted to share their story with anyone, anywhere, and also as a warning.

I initially thought it was by Asimov given the emphasis on chemistry but nothing in his bibliography really jumps out at me.

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This also reminds me of The Hercules Text by Jack McDevitt, 1986.

The message is received with a large radio telescope, the fictional Hercules Array, which was built on the far side of the Moon. It is later discovered that the message was sent with an artificial pulsar built by the alien race. This pulsar with the name Althea has been known by the scientists for years. It was believed to be a normal pulsar. However, what made it special was its almost perfectly regular interval between the observed pulses.

One day, some of the pulses suddenly fail to appear. This incident draws more attention to this particular pulsar, as the newly discovered gaps show a remarkable pattern.

The first gap consists of one missing pulse, the second of two missing pulses and the third gap consists of four missing pulses. The following gaps also consist of numbers representing powers of 2 (2, 4, 8, 16, 32, 64, 128, ...). The transmission of these numbers goes on for a couple of days until the pulsar falls completely silent.

The silence lasts for several weeks, until it breaks again. This time, not just a simple sequence of numbers is received by the Hercules Array. Now, a very large and complex amount of binary data is sent from somewhere close to Althea. Scientists are able to decipher this data. It consists of several mathematical and physical formulae and simple graphical information. Later, more complex information is found, e.g., parts of the sender's DNA, schematics for very advanced technology, philosophical texts or poems.

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This makes me think of The Listeners by James Gunn. The novel was constructed of previously published short stories in various magazines between 1968 and 1972.

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    But the message was a picture, there was no description of a progression of advancing destructive technology, and the sending race was killed by their star dying. It wasn't even a warning, more of a "we were here." And it definitely wasn't based solely on chemistry.
    – DavidW
    Aug 22 at 20:52

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