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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).

%I A340661 #7 Jan 18 2021 18:36:36
%S A340661 4,36,144,361,1369,4225,10816,17689,29929,69169,140625,166464,314721,
%T A340661 474721,729316,1225449,1817104,2353156,3308761,4251844,5832225,
%U A340661 8242641,10942864,13653025,17986081,23396569,28654609,35940025,43243776,53158681,67420521,80622441,97337956
%N 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).
%F A340661 a(n) = A340663(n)^2.
%e A340661 Table of initial terms of a(n), A340662, A340663, A340664, and A340695:
%e A340661     bounded below by       n consecutive squares       terminated by
%e A340661          |             a(n)          A340662(n)           A340695(n)
%e A340661   n      |               |  A340663(n)^2  |  A340664(n)^2   |
%e A340661   1      1 =  1^(>2),    4 =   2^2         4 =   2^2,       8 =  2^ 3
%e A340661   2     32 =  2^ 5,     36 =   6^2 ...    49 =   7^2,      64 =  2^ 6
%e A340661   3    128 =  2^ 7,    144 =  12^2 ...   196 =  14^2,     216 =  6^ 3
%e A340661   4    343 =  7^ 3,    361 =  19^2 ...   484 =  22^2,     512 =  2^ 9
%e A340661   5   1331 = 11^ 3,   1369 =  37^2 ...  1681 =  41^2,    1728 = 12^ 3
%e A340661   6   4096 =  2^12,   4225 =  65^2 ...  4900 =  70^2,    4913 = 17^ 3
%e A340661   7  10648 = 22^ 3,  10816 = 104^2 ... 12100 = 110^2,   12167 = 23^ 3
%e A340661   8  17576 = 26^ 3,  17689 = 133^2 ... 19600 = 140^2,   19683 =  3^ 9
%e A340661   9  29791 = 31^ 3,  29929 = 173^2 ... 32761 = 181^2,   32768 =  2^15
%Y A340661 Cf. A000290, A001597, A111245, A340662, A340663, A340664, A340695.
%K A340661 nonn
%O A340661 1,1
%A A340661 _Hugo Pfoertner_, Jan 18 2021