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%I #30 Sep 08 2022 08:45:06
%S 15,61,245,981,3925,15701,62805,251221,1004885,4019541,16078165,
%T 64312661,257250645,1029002581,4116010325,16464041301,65856165205,
%U 263424660821,1053698643285,4214794573141,16859178292565
%N a(n) = 4*a(n-1) + 1, a(1) = 15.
%C 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).
%C 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
%H Vincenzo Librandi, <a href="/A072201/b072201.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F a(n) = (23*4^n - 2)/6.
%F From _Colin Barker_, Aug 17 2012: (Start)
%F a(n) = 5*a(n-1) - 4*a(n-2).
%F G.f.: x*(15-14*x)/((1-x)*(1-4*x)). (End)
%F a(n) = 46*A002450(n-1) + 15. - _Yosu Yurramendi_, Jan 24 2017
%F a(n) = A178415(8, n) = A347834(6, n-1), arrays, for n >= 1. - _Wolfdieter Lang_, Nov 29 2021
%t NestList[4#+1&,15,20] (* _Harvey P. Dale_, Aug 16 2011 *)
%o (Magma) [(23*4^n-2)/6: n in [1..30]]; // _Vincenzo Librandi_, Aug 17 2011
%Y Cf. A002450, A178415, A347834.
%K nonn,easy
%O 1,1
%A N. Rathankar (rathankar(AT)yahoo.com), Jul 03 2002
%E Edited and extended by _Henry Bottomley_, Aug 05 2002
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