

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.


5



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
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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



