The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A372289

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Showing entries 1-10 | older changes

A372289

a(n) = n*(2^e) + ((4^e)-1)/3, where e is the 2-adic valuation of n.
(history; published version)

#19 by Alois P. Heinz at Sat Apr 27 16:46:27 EDT 2024

STATUS

proposed

approved

#18 by Peter Luschny at Sat Apr 27 05:59:09 EDT 2024

STATUS

editing

proposed

#17 by Peter Luschny at Sat Apr 27 05:58:46 EDT 2024

DATA

1, 5, 3, 21, 5, 13, 7, 85, 9, 21, 11, 53, 13, 29, 15, 341, 17, 37, 19, 85, 21, 45, 23, 213, 25, 53, 27, 117, 29, 61, 31, 1365, 33, 69, 35, 149, 37, 77, 39, 341, 41, 85, 43, 181, 45, 93, 47, 853, 49, 101, 51, 213, 53, 109, 55, 469, 57, 117, 59, 245, 61, 125, 63, 5461, 65, 133, 67, 277, 69, 141, 71, 597, 73, 149, 75

MAPLE

a := proc(n) padic[ordp](n, 2): n*2^% + ((2^%)^2 - 1)/3 end:

seq(a(n), n = 1..64); # Peter Luschny, Apr 27 2024

STATUS

proposed

editing

#16 by Chai Wah Wu at Fri Apr 26 18:32:50 EDT 2024

STATUS

editing

proposed

Discussion

Fri Apr 26

19:08

Alois P. Heinz: I have seen this before ... 
https://oeis.org/history/view?seq=A371949&v=49

Sat Apr 27

02:02

Antti Karttunen: Yes, but this time without any speculative comments.

05:34

Antti Karttunen: Note: whether trying to prove or disprove Ali's original claims, this sequence is good to have at hand as a reference. Also, it has some interest of its own.

05:57

Peter Luschny: Wonderful, this allows me to recycle my function from a recycled sequence.

#15 by Chai Wah Wu at Fri Apr 26 18:32:46 EDT 2024

PROG

(Python)

def A372289(n): return (n<<(e:=(~n & n-1).bit_length()))+((1<<(e<<1))-1)//3 # Chai Wah Wu, Apr 26 2024

STATUS

approved

editing

#14 by Michael De Vlieger at Fri Apr 26 14:33:49 EDT 2024

STATUS

proposed

approved

#13 by Antti Karttunen at Fri Apr 26 12:29:36 EDT 2024

STATUS

editing

proposed

#12 by Antti Karttunen at Fri Apr 26 12:29:21 EDT 2024

FORMULA

For n >= 0, a(2n+1) = 2n+1.

CROSSREFS

Cf. A000265, A005408 (odd bisection), A007814, A371094 [= a(3n+1)].

STATUS

proposed

editing

Discussion

Fri Apr 26

12:29

Antti Karttunen: Added.

#11 by Stefano Spezia at Fri Apr 26 12:24:37 EDT 2024

STATUS

editing

proposed

#10 by Stefano Spezia at Fri Apr 26 12:23:53 EDT 2024

MATHEMATICA

a[n_]:=n*(2^IntegerExponent[n, 2]) + ((4^IntegerExponent[n, 2]) - 1)/3; Array[a, 75] (* Stefano Spezia, Apr 26 2024 *)

STATUS

proposed

editing

Discussion

Fri Apr 26

12:24

Stefano Spezia: a(n) = n for odd n