A340661 -id:A340661 - cp's OEIS frontend

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

Hugo Pfoertner, Jan 18 2021

nonn

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

			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)

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

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

PARI
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\\ See Corneth link
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A340662 a(n) is the end of the first occurrence of n consecutive perfect powers, all of which are squares with exponents equal to 2 (A111245).

Original entry on oeis.org

4, 49, 196, 484, 1681, 4900, 12100, 19600, 32761, 73984, 148225, 175561, 328329, 492804, 753424, 1258884, 1860496, 2405601, 3374569, 4330561, 5929225, 8363664, 11088900, 13823524, 18190225, 23639044, 28933641, 36264484, 43612816, 53582400, 67914081, 81180100, 97970404

Offset: 1

Hugo Pfoertner, Jan 18 2021

nonn

			See A340661.

Cf. A000290, A001597, A111245, A340661, A340663, A340664, A340695.

a(n) = A340664(n)^2 = A340663(n)^2 + (n - 1)*(2*A340663(n) + n - 1).

A340663 a(n)^2 is the start of the first occurrence of n consecutive perfect powers, all of which are squares with exponents equal to 2 (A111245).

Original entry on oeis.org

2, 6, 12, 19, 37, 65, 104, 133, 173, 263, 375, 408, 561, 689, 854, 1107, 1348, 1534, 1819, 2062, 2415, 2871, 3308, 3695, 4241, 4837, 5353, 5995, 6576, 7291, 8211, 8979, 9866, 10880, 11995, 12934, 14113, 15326, 16572, 17889, 19159, 20663, 22289, 23869, 25750, 27361

Offset: 1

Hugo Pfoertner, Jan 18 2021

nonn

			See A340661.

Cf. A000290, A001597, A111245, A340661, A340662, A340664, A340695.

a(n) = sqrt(A340661(n)).

A340664 a(n)^2 is the end of the first occurrence of n consecutive perfect powers, all of which are squares with exponents equal to 2 (A111245).

Original entry on oeis.org

2, 7, 14, 22, 41, 70, 110, 140, 181, 272, 385, 419, 573, 702, 868, 1122, 1364, 1551, 1837, 2081, 2435, 2892, 3330, 3718, 4265, 4862, 5379, 6022, 6604, 7320, 8241, 9010, 9898, 10913, 12029, 12969, 14149, 15363, 16610, 17928, 19199, 20704, 22331, 23912, 25794, 27406

Offset: 1

Hugo Pfoertner, Jan 18 2021

nonn

			See A340661.

Cf. A000290, A001597, A111245, A340661, A340662, A340663, A340695.

a(n) = sqrt(A340662(n)) = A340663(n) + n - 1.

cp's OEIS Frontend

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.

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PARI

A340662 a(n) is the end of the first occurrence of n consecutive perfect powers, all of which are squares with exponents equal to 2 (A111245).

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A340663 a(n)^2 is the start of the first occurrence of n consecutive perfect powers, all of which are squares with exponents equal to 2 (A111245).

Views

Author

Keywords

Examples

Crossrefs

Formula

A340664 a(n)^2 is the end of the first occurrence of n consecutive perfect powers, all of which are squares with exponents equal to 2 (A111245).

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Author

Keywords

Examples

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Formula