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 A385643 #8 Jul 09 2025 18:57:56 %S A385643 1,5,14,16,41,43,47,49,122,124,128,130,140,142,146,148,365,367,371, %T A385643 373,383,385,389,391,419,421,425,427,437,439,443,445,1094,1096,1100, %U A385643 1102,1112,1114,1118,1120,1148,1150,1154,1156,1166,1168,1172,1174,1256,1258,1262 %N A385643 Galileo sequence with ratio k = 5: a(1) = 1, a(2) = k, a(2*n-1) = floor(((k + 1)*a(n) -1)/2), and a(2*n) = floor((k + 1)*a(n)/2) + 1 for n > 2. %C A385643 Solution to Exercise 1.2.3 on page 35 in Tattersall. %C A385643 A Galileo sequence of ratio k > 0 has the property that 1/k = a(1)/a(2) = (a(1) + a(2))/(a(3) + a(4)) = (a(1) + a(2) + a(3))/(a(4) + a(5) + a(6)) = ... %D A385643 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, pages 23, 35. %H A385643 Stefano Spezia, <a href="/A385643/b385643.txt">Table of n, a(n) for n = 1..10000</a> %e A385643 1/5 = (1 + 5)/(14 + 16) = (1 + 5 + 14)/(16 + 41 + 43) = ... %t A385643 k=5; a[1]=1; a[2]=k; a[n_]:=a[n]=If[OddQ[n], Floor[((k+1)*a[(n+1)/2]-1)/2], Floor[(k+1)*a[n/2]/2]+1]; Array[a, 51] %Y A385643 Similar sequences for k=1..5: A037861, A385610, A005408 [Galileo, 1615], A385587, this sequence. %K A385643 nonn,easy,look %O A385643 1,2 %A A385643 _Stefano Spezia_, Jul 06 2025