A002542
Number of two-valued complete Post functions of n variables.
Original entry on oeis.org
0, 2, 56, 16256, 1073709056, 4611686016279904256, 85070591730234615856620279821087277056, 28948022309329048855892746252171976963147354982949671778132708698262398304256
Offset: 1
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- Vincenzo Librandi, Table of n, a(n) for n = 1..11
- Atwell R. Turquette, A General Theory of k-Place Stroke Functions in 2-Valued Logic, Proceedings of the American Mathematical Society 13.5 (1962): 822-824. Gives a(1)-a(4).
- Roger F. Wheeler, Complete connectives for the 3-valued propositional calculus, Proc. London Math. Soc. (3) 16 (1966), 167-191.
- R. F. Wheeler, Complete connectives for the 3-valued propositional calculus, Proc. London Math. Soc. (3) 16 (1966), 167-191. [Annotated scanned copy]
A002857
Number of Post functions of n variables.
Original entry on oeis.org
1, 3, 20, 996, 9333312, 6406603084568576, 16879085743296493582043922521915392, 717956902513121252476003434439730211917452457474409186632352788205535232
Offset: 1
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- Roger F. Wheeler, Complete propositional connectives. Z. Math. Logik Grundlagen Math. 7, 1961, 185-198.
- Alois P. Heinz, Table of n, a(n) for n = 1..12
- Jürgen Heller, Identifiability in probabilistic knowledge structures, J. Math. Psychol. 77, 46-57 (2017).
- R. F. Wheeler, Complete propositional connectives, Z. Math. Logik Grundlagen Math. 7 1961 185-198. [Annotated scanned copy]
- R. F. Wheeler, An asymptotic formula for the number of complete propositional connectives, Z. Math. Logik Grundlagen Math. 8 (1962), 1-4. [Annotated scanned copy]
-
b:= proc(n, i, l) `if`(n=0, 2^(w-> add(mul(2^igcd(t, l[h]),
h=1..nops(l)), t=1..w)/w)(ilcm(l[])), `if`(i<1, 0,
add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i)))
end:
a:= n-> b(n$2, [])/4:
seq(a(n), n=1..8); # Alois P. Heinz, Aug 14 2019
-
b[n_, i_, l_] := If[n==0, 2^Function[w, Sum[Product[2^GCD[t, l[[h]]], {h, 1, Length[l]}], {t, 1, w}]/w][LCM @@ l], If[i < 1, 0, Sum[b[n - i j, i-1, Join[l, Table[i, {j}]]]/j!/i^j, {j, 0, n/i}]]];
a[n_] := b[n, n, {}]/4;
Array[a, 8] (* Jean-François Alcover, Oct 27 2020, after Alois P. Heinz *)
A262546
Number of Post functions of n variables which fail to satisfy Post's second condition.
Original entry on oeis.org
1, 1, 4, 16, 544
Offset: 1
A262547
Nearest integer to 2^(2^n)/(4*n!).
Original entry on oeis.org
1, 2, 11, 683, 8947849, 6405119470038039, 16879085660760836481318184892448820, 717956902513121251386228825698709746114025202539934052824017757985572480
Offset: 1
A262548
Nearest integer to 2^(2^(n-1))/(2*n!).
Original entry on oeis.org
1, 1, 1, 5, 273, 2982616, 1830034134296583, 4219771415190209120329546223112205, 159545978336249166974717516821935499136450045008874233960892835107904996
Offset: 1
Showing 1-5 of 5 results.