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A226722
Positions of the numbers 2^n, for n >=0, in the joint ranking of all the numbers 2^h, 3^k, 5^k, for h >= 0, k >= 1.
4
1, 2, 4, 6, 8, 11, 12, 15, 17, 18, 21, 22, 25, 27, 29, 31, 33, 35, 37, 39, 41, 44, 45, 47, 50, 51, 54, 56, 58, 60, 61, 64, 66, 68, 70, 73, 74, 76, 78, 80, 83, 84, 87, 89, 90, 93, 95, 97, 99, 101, 103, 105, 107, 109, 112, 113, 116, 117, 119, 122, 123, 126
OFFSET
1,2
LINKS
FORMULA
a(n) = n + floor((n-1)*log_3(2)) + floor((n-1)*log_5(2)). [corrected by Jason Yuen, Nov 02 2024]
EXAMPLE
The joint ranking of the powers of 2, 3, 5 begins like this: 1, 2, 3, 4, 5, 8, 9, 16, 25, 27, 32, 64, 81, 125, 128, 243, 256, 512. The numbers 2^n for n >= 0 are in positions 1, 2, 4, 6, 8, 11, 12, 15, 17, 18.
MATHEMATICA
z = 120; b = 2; c = 3; d = 5; f[x_]:=Floor[x];
Table[n + f[(n-1)*Log[c, b]] + f[(n-1)*Log[d, b]], {n, 1, z}] (* this sequence *)
Table[1 + n + f[n*Log[b, c]] + f[n*Log[d, c]], {n, 1, z}] (* A226723 *)
Table[1 + n + f[n*Log[b, d]] + f[n*Log[c, d]], {n, 1, z}] (* A226724 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 16 2013
STATUS
approved