A072201 a(n) = 4*a(n-1) + 1, a(1) = 15.

15, 61, 245, 981, 3925, 15701, 62805, 251221, 1004885, 4019541, 16078165, 64312661, 257250645, 1029002581, 4116010325, 16464041301, 65856165205, 263424660821, 1053698643285, 4214794573141, 16859178292565

Offset: 1

Author

N. Rathankar (rathankar(AT)yahoo.com), Jul 03 2002

Keywords

• nonn
• easy

Comments

These are the integers N which on application of the Collatz function yield the number 23. 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 11).

Numbers whose binary representation is 1111 together with n - 1 times 01. For example, a(4) = 981 = 1111010101 (2). - Omar E. Pol, Nov 24 2012

Links

• Vincenzo Librandi, 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. A002450, A178415, A347834.

Programs

Magma

[(23*4^n-2)/6: n in [1..30]]; // Vincenzo Librandi, Aug 17 2011

Mathematica

NestList[4#+1&,15,20] (* Harvey P. Dale, Aug 16 2011 *)

Formula

a(n) = (23*4^n - 2)/6.

From Colin Barker, Aug 17 2012: (Start)

a(n) = 5*a(n-1) - 4*a(n-2).

G.f.: x*(15-14*x)/((1-x)*(1-4*x)). (End)

a(n) = 46*A002450(n-1) + 15. - Yosu Yurramendi, Jan 24 2017

a(n) = A178415(8, n) = A347834(6, n-1), arrays, for n >= 1. - Wolfdieter Lang, Nov 29 2021

Extensions

Edited and extended by Henry Bottomley, Aug 05 2002