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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 (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

LINKS

Table of n, a(n) for n=2..16.

David Applegate, C++ program used to search for Meertens numbers

Richard S. Bird, Functional Pearl: Meertens number, Journal of Functional Programming 8 (1), Jan 1998, 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

Adjacent sequences:  A246529 A246530 A246531 * A246533 A246534 A246535

KEYWORD

sign,more

AUTHOR

David Applegate, Aug 28 2014

STATUS

approved

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Last modified November 14 01:24 EST 2019. Contains 329108 sequences. (Running on oeis4.)