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

1, 4, 6, 10, 12, 14, 16, 20, 22, 26, 28, 30, 32, 36, 38, 40, 42, 46, 48, 52, 54, 56, 58, 62, 64, 68, 70, 72, 74, 78, 80, 82, 84, 88, 90, 94, 96, 98, 100, 104, 106, 108, 110, 114, 116, 120, 122, 124, 126, 130, 132, 136, 138, 140, 142, 146, 148, 150, 152, 156

Offset: 1

Author

Casey Mongoven, Nov 07 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• C. Kimberling, The first column of an interspersion, Fibonacci Quarterly 32 (1994), pp. 301-314.

Crossrefs

Cf. A199535, A199537.

Programs

Mathematica

a[n_]:= If[Mod[n,2]==0, 2*Floor[(n/2)*GoldenRatio] +n, 2*Floor[(n-1)/2*GoldenRatio] +n+1] -Boole[n==1];
Table[a[n], {n,80}] (* G. C. Greubel, Jun 22 2022 *)

SageMath

def A199536(n):
    if (n==1): return 1
    elif (n%2==0): return 2*floor(n*golden_ratio/2) + n
    else: return 2*floor((n-1)*golden_ratio/2) +n+1
[A199536(n) for n in (1..80)] # G. C. Greubel, Jun 22 2022

Formula

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.

a(n) = A199535(n, n). - G. C. Greubel, Jun 22 2022