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A199536
The first column in Clark Kimberling's even first column Stolarsky array (beginning column count at 1).
3
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
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
Sequence in context: A283564 A348005 A181794 * A284883 A134333 A114331
KEYWORD
nonn
AUTHOR
Casey Mongoven, Nov 07 2011
STATUS
approved