A340695 a(n) is the next perfect power after the earliest occurrence of n consecutive perfect powers, all of which are squares with exponents equal to 2.

8, 64, 216, 512, 1728, 4913, 12167, 19683, 32768, 74088, 148877, 175616, 328509, 493039, 753571, 1259712, 1860867, 2406104, 3375000, 4330747, 5929741, 8365427, 11089567, 13824000, 18191447, 23639903, 28934443, 36264691, 43614208, 53582633, 67917312, 81182737, 97972181

Offset

1,1

Comments

The exponent of a(n) is > 2 thus terminating the progression of n consecutive preceding squares with exponents = 2 (A111245).

Is this sequence strictly increasing? - David A. Corneth, Jan 19 2021

Links

David A. Corneth, Table of n, a(n) for n = 1..6963 (terms <= 10^22)

David A. Corneth, PARI program

Example

See A340661.
From David A. Corneth, Jan 19 2021: (Start)
a(3) = 216 as in the perfect powers we see ..., 128 = 2^7, 144 = 12^2, 169 = 13^2, 196 = 14^2, 216 = 6^3, ... . We write them as powers of m^k where k is chosen as large as possible such that m and k are integers.
Then between two perfect powers with k > 2 (being 128 = 2^7 and 216 = 6^3) we have three consecutive perfect powers with k = 2. As 216 closes this earliest streak of 3, a(3) = 216. (End)

Prog

(PARI) \\ See Corneth link

Crossrefs

Cf. A000290, A001597, A111245, A340661, A340662, A340663, A340664.

Sequence in context: A207393 A207940 A016743 * A086114 A209651 A207071

Adjacent sequences: A340692 A340693 A340694 * A340696 A340697 A340698

Keyword

nonn

Author

Hugo Pfoertner, Jan 18 2021

Status

approved