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

1,1

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = A340663(n)^2.

Example

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

Crossrefs

Cf. A000290, A001597, A111245, A340662, A340663, A340664, A340695.

Sequence in context: A296948 A125756 A173961 * A035287 A183354 A204504

Adjacent sequences: A340658 A340659 A340660 * A340662 A340663 A340664

Keyword

nonn

Author

Hugo Pfoertner, Jan 18 2021

Status

approved