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Looking for the name of an old book I read many years ago back in the early 90's. The book was a slim(ish) novel as I recall, maybe 200 pages?
The book was in English and was probably written in the 1960's, maybe the 1950's.
The concept was about trying to become immortal, and the impact that this desire placed on the fictional society. Immortality was via the use of clones that were given the memories of the original each time they died, rather than perpetual extension of a single life.
The amount of life one had been allotted was recorded by a (mechanical?) computer, and the idea was to extend it by becoming more renowned (there could of been multiple levels of life expectancy).
I remember that the main protagonist (male) was in a fairground with a lady, and they entered an amusement(?) but later she dies while they are sitting in a café.
The protagonist was trying to get into the ranks of the Immortals (as he had been one previously?), he tries some different jobs (hospital porter, assistant to a politician, maybe others) but eventually leaves for space.
The setting was not very defined but was set in a land/city set some time in the future of earth, after some global catastrophe.
Does anyone remember this story? It has a kind of romantic feel to it in my memory