OFFSET
1,1
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).
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
MATHEMATICA
NestList[4#+1&, 15, 20] (* Harvey P. Dale, Aug 16 2011 *)
PROG
(Magma) [(23*4^n-2)/6: n in [1..30]]; // Vincenzo Librandi, Aug 17 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. Rathankar (rathankar(AT)yahoo.com), Jul 03 2002
EXTENSIONS
Edited and extended by Henry Bottomley, Aug 05 2002
STATUS
approved