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a(n) is the smallest number s such that a diagonal form of degree n in s variables with (rational) integer coefficients is guaranteed to have a nontrivial zero in the p-adic fields for all primes p.
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%I #9 Mar 06 2019 08:10:48

%S 2,5,7,17,16,37,22,39,37,101,45,145,53,71,61,257,52,325,58,241,106,

%T 485,116,289,101,157,109,785,146,901,125

%N a(n) is the smallest number s such that a diagonal form of degree n in s variables with (rational) integer coefficients is guaranteed to have a nontrivial zero in the p-adic fields for all primes p.

%H Michael P. Knapp, <a href="https://doi.org/10.1016/j.jnt.2011.04.006">Exact values of the function Gamma*(k)</a>, Journal of Number Theory, Volume 131, Issue 10, October 2011, Pages 1901-1911.

%F a(n) <= n^2+1 with equality if n+1 is prime.

%K nonn,more

%O 1,1

%A _Michel Marcus_, Mar 02 2019