The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A254070

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A254070

a(n) = -1 + (3/2)^(-1 + v(1 + F(4*n - 3)))*(1 + F(4*n - 3)), where v(y) is the 2-adic valuation of y, F(x) = (3*x + 1)/2^v(3*x + 1), and x == 1 (mod 2).
(history; published version)

#31 by OEIS Server at Fri May 10 16:50:59 EDT 2024

LINKS

Ruud H.G. van Tol, <a href="/A254070/b254070_1.txt">Table of n, a(n) for n = 1..10000</a>

#30 by Michael De Vlieger at Fri May 10 16:50:59 EDT 2024

STATUS

reviewed

approved

Discussion

Fri May 10

16:50

OEIS Server: Installed first b-file as b254070.txt.

#29 by Stefano Spezia at Fri May 10 15:57:10 EDT 2024

STATUS

proposed

reviewed

#28 by Ruud H.G. van Tol at Fri May 10 13:21:47 EDT 2024

STATUS

editing

proposed

#27 by Ruud H.G. van Tol at Fri May 10 13:21:25 EDT 2024

LINKS

Ruud H.G. van Tol, <a href="/A254070/b254070_1.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#26 by N. J. A. Sloane at Thu Jul 27 12:13:21 EDT 2023

STATUS

proposed

approved

#25 by Ruud H.G. van Tol at Sat Jul 22 07:56:13 EDT 2023

STATUS

editing

proposed

Discussion

Sat Jul 22

08:09

Ruud H.G. van Tol: The code sets x to 3n-2, and shifts off all 0-bits. It then sets v to the number of trailing 1-bits minus one, shifts those off, and adds one, to produce an even value. Then it multiplies that value with 3^v and subtracts 1, to produce a term. All terms are congruent to 1 (mod 4).

#24 by Ruud H.G. van Tol at Sat Jul 22 07:53:59 EDT 2023

PROG

(PARI) a(n) = my(x=3*n-2, v); x>>=valuation(x, 2)); x>>=v; v=valuation(x+1, 2)-1; ((x>>v)+1)*2*3^(v-1)-1; \\ Ruud H.G. van Tol, Jul 16 2023

STATUS

proposed

editing

Discussion

Sat Jul 22

07:56

Ruud H.G. van Tol: Straightened the PARI-code some more.

#23 by Michel Marcus at Thu Jul 20 01:29:29 EDT 2023

STATUS

editing

proposed

Discussion

Thu Jul 20

08:05

Ruud H.G. van Tol: @Kevin: each ...,15,7,3 (mod 4) only needs one halving, until it reaches 1 (mod 4), so simply is arithmetical. T(4*n-3) = 3*n-2, which can be even, etc.

#22 by Michel Marcus at Thu Jul 20 01:29:22 EDT 2023

MATHEMATICA

v[y_] := IntegerExponent[y, 2]; f[x_] := (3*x + 1)/2^v[3*x + 1]; s[n_] := -1 + (3/2)^(-1 + v[1 + f[4*n - 3]])*(1 + f[4*n - 3]); Table[s[n], {n, 70}] (* - __L. Edson Jeffery_, Mar 29 2021 *)

STATUS

proposed

editing