A072262 a(n) = 4*a(n-1) + 1, a(1)=11.

11, 45, 181, 725, 2901, 11605, 46421, 185685, 742741, 2970965, 11883861, 47535445, 190141781, 760567125, 3042268501, 12169074005, 48676296021, 194705184085, 778820736341, 3115282945365, 12461131781461, 49844527125845

Offset: 1

Author

N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002

Keywords

• nonn
• easy

Comments

These are the integers N which on application of the Collatz function yield the number 17. The Collatz function: if N is an odd number then (3N+1)/2^r yields a positive odd integer for some value of r (which in this case is 17).

Numbers whose binary representation is 1011 together with n - 1 times 01. For example, a(4) = 725 = 1011010101 (2). - Omar E. Pol, Nov 24 2012

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4).
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A072257, A072258, A072259, A072260, A072261, A099730, A178415, A347834.

Programs

GAP

List([1..30], n-> (17*4^n -2)/6); # G. C. Greubel, Jan 14 2020

Magma

[(17*4^n -2)/6: n in [1..30]]; // G. C. Greubel, Jan 14 2020

Maple

seq( (17*4^n -2)/6, n=1..30); # G. C. Greubel, Jan 14 2020

Mathematica

a[n_]:= 4a[n-1] +1; a[1]=11; Table[a[n], {n,25}]
NestList[4#+1&,11,30] (* or *) LinearRecurrence[{5,-4},{11,45},30] (* Harvey P. Dale, Dec 25 2014 *)

PARI

vector(30, n, (17*4^n -2)/6) \\ G. C. Greubel, Jan 14 2020

Sage

[(17*4^n -2)/6 for n in (1..30)] # G. C. Greubel, Jan 14 2020

Formula

From Bruno Berselli, Dec 16 2011: (Start)

G.f.: x*(11-10*x)/(1-5*x+4*x^2).

a(n) = (17*2^(2*n-1) - 1)/3.

Sum_{i=1..n} a(i) = (a(n+1) - n + 1)/3 - 4. (End)

a(n) = 34*A002450(n-1) + 11 . - Yosu Yurramendi, Jan 24 2017

E.g.f.: (-15 - 2*exp(x) + 17*exp(4*x))/6. - G. C. Greubel, Jan 14 2020

a(n) = A178415(6, n) = A347834(5, n-1), arrays, for n >= 1. - Wolfdieter Lang, Nov 29 2021

Extensions

Edited and extended by Robert G. Wilson v, Jul 17 2002