High Quality Content by WIKIPEDIA articles! A Ulam number is a member of an integer sequence which was devised 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. By the definition, 3=1+2 is an Ulam number; and 4=1+3 is an Ulam number (The sum 4=2+2 doesn't count because the previous terms must be distinct.) The integer 5 is not an Ulam number because 5=1+4=2+3. The idea can be generalized as (u, v)-Ulam Numbers by selecting different starting values (u, v) and by requiring that the terms be a sum of "s" previous terms in a given number "t" of ways, referred as an (s, t)-Additive Sequence or as an s-Additive Sequence for the standard case t = 2. Also it has been proved that u(2,v) where v is odd and v>=5 have periodic successive differences.

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