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A246532 Smallest Meertens number in base n, or -1 if none exists. 2
2, 10, 200, 6, 54, 100, 216, 4199040, 81312000, -1, -1, -1, 47250, -1, 18, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
A Meertens number in base n is a fixed point of the base n Godel encoding.
The base n Godel encoding of x is 2^d(1) * 3^d(2) * ... * prime(k)^d(k), where d(1)d(2)...d(k) is the base n representation of x.
The -1 entries are all conjectures.
In a computer search that included all numbers < 10^29 and bases <= 16, the only additional Meertens numbers found were 6 (base 2), 10 (base 2), 49000 (base 5), and 181400 (base 5).
There is no base 11 Meertens number < 11^44 ~= 6.6*10^45.
There is no base 12 Meertens number < 12^40 ~= 1.4*10^43.
There is no base 13 Meertens number < 13^39 ~= 2.7*10^43.
There is no base 15 Meertens number < 15^37 ~= 3.2*10^43.
Other terms: a(17) = 36, a(19) = 96, a(32) = 256, a(51) = 54. - Chai Wah Wu, Aug 28 2014
From Chai Wah Wu, Jul 20 2020: (Start)
All terms are even.
If n > 2 and a(n) != -1, then a(n) > n.
a(2*3^m-m) = 2*3^m for all m >= 0, i.e., a(n) > 0 for an infinite number of values of n.
Other terms: a(64) = a(4096) = 65536, a(71) = 216, a(160) = 324, a(323) = 1296, a(1455) = 2916, a(1942) = 5832, a(7775) = 46656, a(8294) = 82944, a(13118) = 26244.
(End)
Named by Bird (1998) after the Dutch computer scientist Lambert Meertens (b. 1944). - Amiram Eldar, Jun 23 2021
LINKS
Richard S. Bird, Functional Pearl: Meertens number, Journal of Functional Programming, Vol. 8, No. 1 (Jan 1998), pp. 83-88.
Wikipedia, Meertens number.
Chai Wah Wu, Meertens Number and Its Variations, IBM Research Report RC25531 (WAT1504-032), April 2015.
Chai Wah Wu, Meertens Number and Its Variations, arXiv:1603.08493 [math.NT], 2016.
EXAMPLE
100 is a base 7 Meertens number because 100 = 202_7 = 2^2 * 3^0 * 5^2.
4199040 is a base 9 Meertens number because 4199040 = 7810000_9 = 2^7 * 3^8 * 5^1.
CROSSREFS
Cf. A189398 (base 10 Godel encoding), A110765 (base 2 Godel encoding).
Sequence in context: A155200 A264563 A156510 * A159558 A297066 A320395
KEYWORD
sign,more
AUTHOR
David Applegate, Aug 28 2014
EXTENSIONS
a(17) from Chai Wah Wu, Jul 19 2020
STATUS
approved

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Last modified June 23 20:00 EDT 2024. Contains 373653 sequences. (Running on oeis4.)