This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056850 #35 Jun 01 2025 22:16:55
%S A056850 0,1,1,5,17,13,217,139,1631,3299,6487,46075,7153,502829,588665,
%T A056850 2428309,9492289,5077565,118985033,88519643,808182895,1870418611,
%U A056850 2978678759,25423702091,7551629537,252223018333,342842572777,1170495537221,5284606410545,1738366812781
%N A056850 Minimal absolute difference of 3^n and 2^k.
%C A056850 Except for 3^0 - 2^0, 3^1 - 2^1 and 3^2 - 2^3, there are no cases where the differences are less than 4.
%C A056850 It is known that a(n) tends to infinity as n tends to infinity. Indeed, Tijdeman showed that there exists an effectively computable constant c > 0 such that |2^x - 3^y| > 2^x/x^c. - _Tomohiro Yamada_, Sep 29 2017
%C A056850 Empirical observation: For at least values a(0) through a(6308), k-2 < n*log_2(3) < k+2. - _Matthew Schuster_, Mar 28 2021
%C A056850 For all n >= 0, the lower and upper limits on n*log_2(3) - k are log_2(3/4) = -0.4150374... and log_2(3/2) = 0.5849625..., respectively; i.e., 0 <= n*log_2(3) - k - log_2(3/4) < 1. - _Jon E. Schoenfield_, Apr 21 2021
%H A056850 Michael De Vlieger, <a href="/A056850/b056850.txt">Table of n, a(n) for n = 0..2097</a>
%H A056850 R. Tijdeman, <a href="http://www.numdam.org/item?id=CM_1973__26_3_319_0">On integers with many small prime factors</a>, Compos. Math. 26 (1973), 319--330.
%e A056850 For n = 4, the closest power of 2 to 3^n = 81 is 2^6 = 64, so a(4) = |3^4 - 2^6| = |81 - 64| = 17. - _Jon E. Schoenfield_, Sep 30 2017
%t A056850 Table[Min[# - 2^Floor@ Log2@ # &[3^n], 2^Ceiling@ Log2@ # - # &[3^n]], {n, 0, 27}]
%Y A056850 Cf. A056577 (smallest 3^n-2^k), A063003 (smallest 2^k-3^n).
%K A056850 nonn
%O A056850 0,4
%A A056850 _Robert G. Wilson v_, Aug 30 2000
%E A056850 a(28)-a(29) from _Jon E. Schoenfield_, Mar 31 2021