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In my answer here where I suggested Danny Dunn and the Voice from Space, I mentioned the image that the protagonists receive from space via a radio telescope, which was decoded in part because they recognized that the signal consists of 559 "bits", the product of two primes, 13 and 43.

Image of the transmitted message

Someone commented on the similarity to the Arecibo message, which used a similar trick of sending out a message that made an image by using dimensions of two primes, and how this was likely an homage, but as per my reply, much to my surprise, the novel was published in 1967, while the Arecibo message wasn't sent until 1974!

I know that Carl Sagan was consulted for the Arecibo message. I assume that the idea of using two primes to increase the likelihood that an intelligent civilization would try interpreting it as a grid image existed somewhere in the scientific literature, which Raymond Abrashkin and Jay Williams, as well as the composers of the Arecibo message, drew upon, but I'm not finding any evidence of that yet. Or did Raymond Abrashkin and Jay Williams come up with it, and then it was used for the Arecibo message?

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    While it is safe to assume the Franke Drake role. A bit of digging turned up the prime raster grid art idea was originated by his colleague Bernard M. Oliver shortly after a 1961 conference. Source Communication with Extraterrestrial Intelligence by LD CALLIMAHOS (1965 ?) nsa.gov/portals/75/documents/news-features/… or original article photocopy media.defense.gov/2021/Jul/13/2002761372/-1/-1/0/…
    – lucasbachmann
    Feb 25 at 0:54
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    At first glance it would appear the message says "A crab monster alien from a binary star system is taking a rocket invasion fleet to a 9 planet solar system". But I'm no Danny Dunn.
    – lucasbachmann
    Feb 25 at 2:33
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    @chasly-supportsMonica: Maybe the planet orbits the star represented on the left of the binary system?
    – Nick Matteo
    Feb 25 at 16:56
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    That is the case. The two stars depicted are identified in the book as 61 Cygni A and B, with a mutual orbital period on the order of 680 years, and both are K-Class, so any world warm enough for liquid water would orbit only one of the stars, fairly close. (Also, Sir Edward, one of the characters in the book believes that the planet orbits one of them.)
    – notovny
    Feb 25 at 17:54
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    @chasly-supportsMonica with only 559 pixels - that does certainly limit accuracy. The Arecibo message message has our solar system all in a line with Earth offset to single it out. Though an alien may wonder why it's orbit was off plane!
    – lucasbachmann
    Feb 25 at 22:50

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I think it's likely that the book was inspired by the preliminary thoughts that Frank Drake had before actually sending his message. Evidence: Drake is mentioned by the characters in the book itself, and credited by the authors for his help, as mentioned in this discussion:

Danny Dunn in 'Danny Dunn and the Voice from Space' visits a radio telescope in England that closely resembles the one at Jodrell Bank. His experiences have a certain authenticity because the author acknowledges assistance from Frank Drake, a respected American astronomer closely involved with the SETI project, the Search for Extra-Terrestrial Intelligence.

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    That's good enough for me. :)
    – FuzzyBoots
    Feb 24 at 21:43

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