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URL: https://oeis.org/A004143

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A004143
From the powers that be.
1
0, 1, 2, 5, 10, 40, 40, 105, 5627, 14501, 330861, 658110, 897229, 26673531, 180566007, 180566007, 19299107624
OFFSET
1,3
COMMENTS
For n>0, let b be the smallest nonnegative integer such that 2^m_1 > 3^m_2 > ... > prime(n)^m_n, where m_i is the exponent satisfying prime(i)^m_i <= b < prime(i)^(m_i+1). This sequence records the exponent m_1 for b because b=2^m_1. - Tom Edgar, Dec 05 2014
Equivalently, a(n) is the first k such that p^frac(k/log_2(p)) is increasing over the first n primes. - Charlie Neder, Nov 03 2018
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. B. Eggleton, P. Erdős and J. L. Selfridge, The powers that be, Amer. Math. Monthly, 83 (1976), 801-805.
EXAMPLE
From Sean A. Irvine, Dec 22 2015: (Start)
a(8) = 105 from the chain of powers
2^105 > 3^66 > 5^45 > 7^37 > 11^30 > 13^28 > 17^25 > 19^24,
with each power satisfying p_i^{m_i} <= 2^105 < p_i^{m_i+1}. (End)
From Don Reble, Dec 22 2015: (Start)
An independent calculation verifies these results:
2: 1 0
3: 2 1 0
4: 5 3 2 1
5: 10 6 4 3 2
6: 40 25 17 14 11 10
7: 40 25 17 14 11 10 9
8: 105 66 45 37 30 28 25 24
9: 5627 3550 2423 2004 1626 1520 1376 1324 1243
10: 14501 9149 6245 5165 4191 3918 3547 3413 3205 2984
11: 330861 208750 142494 117855 95640 89411 80945 77887 73141 68106 66783
12: 658110 415221 283432 234423 190236 177846 161006 154924 145484
135469 132838 126329
13: 897229 566088 386415 319599 259357 242465 219507 211215 198345
184691 181104 172230 167469 (End)
CROSSREFS
Cf. A266162 (erroneous version).
Sequence in context: A363429 A290032 A155217 * A266162 A103036 A018439
KEYWORD
nonn,nice,more
EXTENSIONS
Offset, a(8) corrected and a(13) from Sean A. Irvine, Dec 22 2015
a(14)-a(16) from Charlie Neder, Nov 04 2018
a(15) corrected, a(14) and a(16) confirmed, and a(17) from Bert Dobbelaere, Dec 26 2018
STATUS
approved