What is the earliest mention of doubling grains on a chessboard story?

Question

This is a story that seems to be an obligatory mention in either sequence and series lessons or exponential functions and today I've decided to track down the transmission of this story. it goes like this:

One of the most famous legends about series concerns the long inventor of chess whose name is lost the ages. According to the legend, an Indian king summoned the inventor and suggested that he chose the award for the creation of the interesting and wise game. The king was amazed by the “modest” request from the inventor who asked to give him for the first cell of the chessboard 1 grain of wheat, for the second—2 grains, for the third—4 grains, for the fourth—twice as much as in the previous cell, etc. As a result, the total number of grains per 64 cells of the chessboard would be number 18,446,744,073,709,551,615 (18 quintillion, 446 quadrillion, 744 trillion, 73 billion, 709 million, and 551,615). If the king was able to have that much of wheat, he would have to plant it everywhere on the entire surface of the Earth including the territories of the seas and oceans, and mountains, and the desert, from the Arctic to the Antarctic in order obtain a satisfactory harvest, then, perhaps, he maybe could pay his amazing debt off to the chess inventor in over 5 years.
[ Methods of Solving Sequence and Series Problems - Ellina Grigorieva pg191 ]

This is not exactly a hard hitting question but it would be nice to know at least the earliest mention of the story.

Answer 1

The name is not lost to the ages, it was made up along with the rest of this fable. Sissa ben Dahir, an Indian brahmin or grand vizier, supposedly invented chaturanga, a predecessor of chess, somewhere between 400 and 600 AD.

Some prehistory is described in What is the origin of the "wheat and chessboard" legend? on History SE. Adding up terms of a doubling series can be traced to a cuneiform tablet c. 1800 BC, without connection to yet to be invented chess, but with grains and plausible transmission to India and Persia, where it was attached to chessboards centuries later. Hoyrup translates it thus:"1 grain has appended 1 grain: 2 grains the first day. 4 grains the 2nd day. 8 grains the 3d day. 16 grains the 4th day... and so on until 30 days."

The chess fable proper goes back to Islamic sources, which is why the Indian brahmin has the Arabic sounding name. Murray names several manuscripts mentioning Sissa in his History of Chess, one already copied c. 996 AD, so the fable is older. Macdonell mentions Ibn Khallikan's retelling c. 1250 AD, without Sissa and with corn instead of wheat. He also describes several other chess related tales from c. 950 AD onwards. For example, an alternative chess origin myth, with no grains at all, but with two brothers vying for the Indian throne, is told in Firdausi's famous poem Shahnameh written after 977 AD. Second half of the 10th century is when chess became popular in the Islamic world, and tales about it got made and remade.