cp's OEIS Frontend

A199536 The first column in Clark Kimberling's even first column Stolarsky array (beginning column count at 1).

%I A199536 #31 Jan 05 2025 19:51:39
%S A199536 1,4,6,10,12,14,16,20,22,26,28,30,32,36,38,40,42,46,48,52,54,56,58,62,
%T A199536 64,68,70,72,74,78,80,82,84,88,90,94,96,98,100,104,106,108,110,114,
%U A199536 116,120,122,124,126,130,132,136,138,140,142,146,148,150,152,156
%N A199536 The first column in Clark Kimberling's even first column Stolarsky array (beginning column count at 1).
%H A199536 G. C. Greubel, <a href="/A199536/b199536.txt">Table of n, a(n) for n = 1..5000</a>
%H A199536 C. Kimberling, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/32-4/kimberling.pdf">The first column of an interspersion</a>, Fibonacci Quarterly 32 (1994), pp. 301-314.
%F A199536 Define Phi = (1+sqrt(5))/2, then a(1) = 1, a(2*n) = 2*floor(n*Phi) + 2*n, a(2*n+1) = 2*floor(n*Phi) + 2*n + 2.
%F A199536 a(n) = A199535(n, n). - _G. C. Greubel_, Jun 22 2022
%t A199536 a[n_]:= If[Mod[n,2]==0, 2*Floor[(n/2)*GoldenRatio] +n, 2*Floor[(n-1)/2*GoldenRatio] +n+1] -Boole[n==1];
%t A199536 Table[a[n], {n,80}] (* _G. C. Greubel_, Jun 22 2022 *)
%o A199536 (SageMath)
%o A199536 def A199536(n):
%o A199536     if (n==1): return 1
%o A199536     elif (n%2==0): return 2*floor(n*golden_ratio/2) + n
%o A199536     else: return 2*floor((n-1)*golden_ratio/2) +n+1
%o A199536 [A199536(n) for n in (1..80)] # _G. C. Greubel_, Jun 22 2022
%Y A199536 Cf. A199535, A199537.
%K A199536 nonn
%O A199536 1,2
%A A199536 _Casey Mongoven_, Nov 07 2011