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 A385587 #15 Jul 09 2025 18:57:41 %S A385587 1,4,9,11,22,23,27,28,54,56,57,58,67,68,69,71,134,136,139,141,142,143, %T A385587 144,146,167,168,169,171,172,173,177,178,334,336,339,341,347,348,352, %U A385587 353,354,356,357,358,359,361,364,366,417,418,419,421,422,423,427,428,429 %N A385587 Galileo sequence with ratio k = 4: 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 A385587 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)) = ... %C A385587 In Tattersall reference the terms a(7) = 27 and a(8) = 28 miss. %D A385587 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 23. %H A385587 Stefano Spezia, <a href="/A385587/b385587.txt">Table of n, a(n) for n = 1..10000</a> %e A385587 1/4 = (1 + 4)/(9 + 11) = (1 + 4 + 9)/(11 + 22 + 23) = ... %t A385587 k=4; 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,57] %Y A385587 Similar sequences for k=1..5: A037861, A385610, A005408 [Galileo, 1615], this sequence, A385643. %K A385587 nonn,easy,look %O A385587 1,2 %A A385587 _Stefano Spezia_, Jul 03 2025