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 A073698 a(n) is smallest prime not already in the sequence such that the sum of the first n terms is an n-th power. 3
 2, 7, 503, 113, 7151, 109873, 162287, 2251875110689, 1423309560546093919, 1831931738588396657, 266306005917953213327, 13573982207668041076860262513, 4485809513902758532742979512207 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE Sum of two terms 2+7 = 9 = 3^2. Sum of three terms 2+7+503 = 512 = 8^3. MATHEMATICA a[n_] := a[n]=Module[{sm, i}, sm=Sum[a[i], {i, 1, n-1}]; For[k=Ceiling[(sm+2)^(1/n)], !ProvablePrimeQ[k^n-sm]||MemberQ[a/@Range[n-1], k^n-sm], k++, Null]; k^n-sm] (* First do <

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Last modified July 17 18:47 EDT 2019. Contains 325109 sequences. (Running on oeis4.)