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

1,2

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.

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

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 *)

Prog

(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

Crossrefs

Cf. A199535, A199537.

Sequence in context: A283564 A348005 A181794 * A284883 A134333 A114331

Adjacent sequences: A199533 A199534 A199535 * A199537 A199538 A199539

Keyword

nonn

Author

Casey Mongoven, Nov 07 2011

Status

approved