Least k > 1 so that k^n + (k-1)^n >= (k+1)^n + 1^n.
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 115, 117, 119, 121, 123, 125, 127, 129, 131
1
Note that this function is not quite linear; there are occasionally differences of 3. The first occurs at n=16.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(Mma) Table[k = 2; While[k^pwr + (k - 1)^pwr < (k + 1)^pwr + 1, k++]; k, {pwr, 100}]
nonn
T. D. Noe, Apr 21 2015