A132187 -id:A132187 - cp's OEIS frontend

A132183 Number of "regular" Boolean functions of n variables.

2, 3, 5, 10, 27, 119, 1173, 44315, 16175190, 284432730176

Offset: 0

Don Knuth, Nov 19 2007

The sequence also counts order ideals (or antichains) of the binary majorization lattice with 2^n points. That lattice for n=5 will be illustrated in Fig. 8 of Volume 4 of The Art of Computer Programming. The basic properties of this lattice will be discussed in exercise 7.1.1-109 of that book. (The material of Section 7.1.1 will be available in paperback in a couple months.)
Michael Somos (Mar 13 2012) asks if A003187 and A132187 are the same. - N. J. A. Sloane, Mar 13 2012
For n from 1 to 8, a(n) agrees with the number of directed games on n players in Table 1 of Krohn and Sudhölter. - Peter Bala, Dec 16 2021

			For example, the 10 Boolean functions for n=3 have the truth tables
  00000000
  00000001
  00000011
  00000111
  00001111
  00010111
  00011111
  00111111
  01111111
  11111111
(things don't get very interesting until n=4 or 5).

Stefan Bolus, A QOBDD-based Approach to Simple Games, Dissertation, Doktor der Ingenieurwissenschaften der Technischen Fakultaet der Christian-Albrechts-Universitaet zu Kiel, 2012. - From _N. J. A. Sloane_, Dec 22 2012
Bjørn Kjos-Hanssen, Lei Liu, The number of languages with maximum state complexity, arXiv:1902.00815 [cs.FL], 2019.
I. Krohn and P. Sudhölter, Directed and weighted majority games, Mathematical Methods of Operation Research, 42, 2 (1995), 189-216. See Table 1, row 1, p. 213; also on ResearchGate.

Cf. A003187.

A132185 a(n) is the largest number beginning with 1 such that, for any m, the number formed from the first m digits of a(n) is congruent to n mod m.

Original entry on oeis.org

144408645048225636603816, 1725676121534561296189, 188276429246387492222, 19838179232721317143537, 12764828245698443284086, 176903816597810123057, 18626438463030625206604, 19352559475935751347112, 16128296082816884008108

Offset: 0

Philippe LALLOUET (philip.lallouet(AT)orange.fr), Nov 04 2007

Obviously, each such number has at least ten digits; thence one can extend with diminishing probability. But a(211131)=1715193991236363935195556991413939 has 34 digits!

			a(3) = 19838179232721317143537 because 19 == 3 mod 2, 198 == 3 mod 3, 1983 == 3 mod 4,..., 19838179232721317143537 == 3 mod 23; but no additional digit makes a 3 mod 24 number.

Cf. A051883, A109032, A113538, A132187, A134595.

Edited by Don Reble, Nov 07 2007

A134595 a(n) is the smallest number such that, for any m, the number formed from the first m digits of a(n) is congruent to n mod m; but no digit can be appended to maintain the condition.

Original entry on oeis.org

1080548820, 1121114531, 1010249842, 1115859543, 1064928464, 1105018975, 1026605496, 1303211957, 1012880068, 1113933789, 1002529000, 1139156391, 1080784472, 1121350183, 1010485494, 1111055105, 1000603246, 1101719337

Offset: 0

Philippe LALLOUET (philip.lallouet(AT)orange.fr), Nov 04 2007

Obviously, each such number has at least ten digits. Smaller numbers (like 1020005640 for 0 mod m) can be extended (to 10200056405).

			a(1) = 1121114531 because 11 == 1 mod 2, 112 == 1 mod 3, 1211 == 1 mod 4, ..., 1121114531 == 1 mod 10 but there is no digit such that 1121114531d == 1 mod 11. (10 is not a digit.)

Cf. A051883, A132185, A132187.

Edited by Don Reble, Nov 07 2007

cp's OEIS Frontend

A132183 Number of "regular" Boolean functions of n variables.

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A132185 a(n) is the largest number beginning with 1 such that, for any m, the number formed from the first m digits of a(n) is congruent to n mod m.

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A134595 a(n) is the smallest number such that, for any m, the number formed from the first m digits of a(n) is congruent to n mod m; but no digit can be appended to maintain the condition.

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