A051633 a(n) = 5*2^n - 2.

3, 8, 18, 38, 78, 158, 318, 638, 1278, 2558, 5118, 10238, 20478, 40958, 81918, 163838, 327678, 655358, 1310718, 2621438, 5242878, 10485758, 20971518, 41943038, 83886078, 167772158, 335544318, 671088638, 1342177278, 2684354558, 5368709118, 10737418238, 21474836478

Offset

0,1

Comments

For n>=1, when the Collatz map A006370 is applied to a(n) for n-1 steps, the least significant digit will cycle from 8 to 9 back to 8 exactly n-1 times before turning into a 4, and each term is the smallest number that fits such criteria. For a(3) = 38 we get 38 -> 19 (1st 9) -> 58 -> 29 (2nd 9) -> 88 -> 44 (no 9). - Nikolas Grosland, Jun 14 2026

Links

Stefano Spezia, Table of n, a(n) for n = 0..3300

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

a(n) = A118654(n, 5).

a(n) = A000079(n)*5 - 2 = A020714(n) - 2. - Omar E. Pol, Dec 23 2008

a(n) = 2*(a(n-1)+1) with a(0)=3. - Vincenzo Librandi, Aug 06 2010

a(n) = A123208(2*n+1) = A048487(n)+2 = A131051(n+2) = A153894(n)-1. - Philippe Deléham, Apr 15 2013

G.f.: ( 3-x ) / ( (2*x-1)*(x-1) ). - R. J. Mathar, Mar 23 2023

E.g.f.: exp(x)*(5*exp(x) - 2). - Stefano Spezia, Oct 03 2023

Example

a(4) = 5*2^4 - 2 = 80 - 2 = 78.

Mathematica

LinearRecurrence[{3, -2}, {3, 8}, 30] (* Ray Chandler, Jul 18 2020 *)

Prog

(PARI) a(n) = 5<<n-2; \\ Bruce Nye, Jun 24 2026

Crossrefs

Cf. A000079, A020714, A118654.

Cf. A123208, A048487, A131051, A153894.

Cf. A006370.

Sequence in context: A000235 A006478 A104187 * A131051 A172265 A258272

Adjacent sequences: A051630 A051631 A051632 * A051634 A051635 A051636

Keyword

easy,nonn,changed

Author

Asher Auel

Status

approved