A340661 a(n) is the start of the first occurrence of n consecutive perfect powers, all of which are squares with exponents equal to 2 (A111245).
4, 36, 144, 361, 1369, 4225, 10816, 17689, 29929, 69169, 140625, 166464, 314721, 474721, 729316, 1225449, 1817104, 2353156, 3308761, 4251844, 5832225, 8242641, 10942864, 13653025, 17986081, 23396569, 28654609, 35940025, 43243776, 53158681, 67420521, 80622441, 97337956
Offset: 1
Keywords
Examples
Table of initial terms of a(n), A340662, A340663, A340664, and A340695:
bounded below by n consecutive squares terminated by
| a(n) A340662(n) A340695(n)
n | | A340663(n)^2 | A340664(n)^2 |
1 1 = 1^(>2), 4 = 2^2 4 = 2^2, 8 = 2^ 3
2 32 = 2^ 5, 36 = 6^2 ... 49 = 7^2, 64 = 2^ 6
3 128 = 2^ 7, 144 = 12^2 ... 196 = 14^2, 216 = 6^ 3
4 343 = 7^ 3, 361 = 19^2 ... 484 = 22^2, 512 = 2^ 9
5 1331 = 11^ 3, 1369 = 37^2 ... 1681 = 41^2, 1728 = 12^ 3
6 4096 = 2^12, 4225 = 65^2 ... 4900 = 70^2, 4913 = 17^ 3
7 10648 = 22^ 3, 10816 = 104^2 ... 12100 = 110^2, 12167 = 23^ 3
8 17576 = 26^ 3, 17689 = 133^2 ... 19600 = 140^2, 19683 = 3^ 9
9 29791 = 31^ 3, 29929 = 173^2 ... 32761 = 181^2, 32768 = 2^15
Formula
a(n) = A340663(n)^2.