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).

1, 1, 17, 5, 13, 1, 29, 17, 25, 17, 161, 17, 37, 5, 65, 53, 49, 13, 125, 29, 61, 1, 101, 53, 73, 29, 269, 41, 85, 17, 137, 161, 97, 25, 233, 53, 109, 17, 173, 89, 121, 161, 1457, 65, 133, 17, 209, 161, 145, 37, 341, 77, 157, 5, 245, 125, 169, 65, 593, 89, 181, 53, 281, 485, 193, 49, 449, 101, 205, 13

Offset: 1

Author

L. Edson Jeffery, May 03 2015

Keywords

• nonn

Comments

a(n) is the first successor in the 3x+1 trajectory of 4*n-3 that is congruent to 1 mod 4. - Ruud H.G. van Tol, Jul 16 2023

Links

• Ruud H.G. van Tol, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A257480, A253676, A254068.

Programs

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 *)

PARI

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

Formula

a(n) = 4*A257480(n) - 3. - L. Edson Jeffery, Mar 29 2021

Extensions

New name by L. Edson Jeffery, Mar 29 2021