ulam numbers

     

A Ulam number is a member of an integer sequence which was evised by Stanislaw Ulam and published in SIAM Review in 1964. The standard Ulam sequence (the (1, 2)-Ulam sequence) starts with U1=1 and U2=2 being the first two Ulam numbers. Then for n > 2, Un is defined to be the smallest integer that is the sum of two distinct earlier terms in exactly one way (Guy 2004:166-67). Ulam conjectured that the numbers have zero density, but they seem to have a density of approximately 0.07396.

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