A216472 Smallest k such that k*n^5 + 1 is an n-th power.
1, 7, 2269, 4129151, 30762501251, 2239747210, 27448639374405504361, 2413133306001931169183743, 382044091289242990177493431399, 92389875896827641843360078, 41175701028835553188828526348886198418157, 251171485090270512606177135871202294053615
Offset: 1
Keywords
Examples
a(3) = 2269 because 2269*3^5 + 1 = 551368 = 82^3.
Programs
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Mathematica
a={}; Do[k = 2; While[ !IntegerQ[(k^n - 1)/n^5], k++ ]; AppendTo[a, (k^n-1)/n^5], {n, 1, 20}]; a