log(m)'s close to integers, various log bases

[Dean Hickerson]

At Neil Sloane's request, I've formatted the sequences with bases e, pi,
and phi for the OEIS.  Please let me know if you spot any errors.

%I A080021
%S A080021 2,3,7,20,148,403,1096,1097,2980,2981,8103,59874,162755,442413,1202604,
%T A080021 3269017,8886110,8886111,24154952,24154953,65659969,178482301,
%U A080021 3584912846,9744803446,26489122130,72004899337,195729609428
%N A080021 log(n) is closer to an integer than is log(m) for any m with 2<=m<n.
%C A080021 Every term is floor(e^k)+r for some integers k and r with k>=1 and -1 <= r <= 1.
%D A080021 Suggested by Leroy Quet (qqquet at mindspring.com), Jan 19 2003
%e A080021 log(2) = 1-0.306..., log(3) = 1+0.0986..., log(7) = 2-0.0540..., log(20) = 3-0.00426...
%Y A080021 Cf. A080022, A080023.
%K A080021 nonn,new
%O A080021 0,1
%A A080021 Dean Hickerson (dean at math.ucdavis.edu), Jan 20 2003
%E A080021 More terms from Don Reble (djr at nk.ca), Jan 20 2003

%I A080022
%S A080022 2,3,10,31,306,9488,9489,29808,29809,93648,294204,9122171,28658146,
%T A080022 888582403,8769956796,27551631843,86556004192,854273519914,
%U A080022 2683779414318,8431341691876,26487841119103,26487841119104
%N A080022 log_pi(n) is closer to an integer than is log_pi(m) for any m with 2<=m<n.
%C A080022 Every term is floor(pi^k)+r for some integers k and r with k>=1 and -1 <= r <= 1.
%D A080022 Suggested by Neil Fernandez (primeness at borve.demon.co.uk), Jan 19 2003
%e A080022 log_pi(2) = 1-0.394..., log_pi(3) = 1-0.0402..., log_pi(10) = 2+0.0114..., log_pi(31) = 3-0.000176...
%Y A080022 Cf. A080021, A080023.
%K A080022 nonn,new
%O A080022 0,1
%A A080022 Dean Hickerson (dean at math.ucdavis.edu), Jan 20 2003

%I A080023
%S A080023 2,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778,9349,
%T A080023 15127,24476,39603,64079,103682,167761,271443,439204,710647,1149851,
%U A080023 1860498,3010349,4870847,7881196,12752043,20633239,33385282,54018521
%N A080023 log_phi(n) is closer to an integer than is log_phi(m) for any m with 2<=m<n, where phi=(1+sqrt(5))/2 is the golden ratio.
%C A080023 This is the sequence of Lucas numbers (A000032) without the term 1.
%D A080023 Suggested by Neil Fernandez (primeness at borve.demon.co.uk), Jan 19 2003
%e A080023 log_phi(2) = 1+0.440..., log_phi(3) = 2+0.283..., log_phi(4) = 3-0.119..., log_phi(7) = 4+0.0437...
%Y A080023 Cf. A000032, A080021, A080022.
%K A080023 nonn,easy,new
%O A080023 0,1
%A A080023 Dean Hickerson (dean at math.ucdavis.edu), Jan 20 2003

Dean Hickerson
dean at math.ucdavis.edu