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A072201 a(n) = 4*a(n-1) + 1, a(1) = 15. 1
15, 61, 245, 981, 3925, 15701, 62805, 251221, 1004885, 4019541, 16078165, 64312661, 257250645, 1029002581, 4116010325, 16464041301, 65856165205, 263424660821, 1053698643285, 4214794573141, 16859178292565 (list; graph; refs; listen; history; text; internal format)
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

Sequence in context: A284096 A022288 A041432 * A218811 A219819 A157446

Adjacent sequences:  A072198 A072199 A072200 * A072202 A072203 A072204

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

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Last modified February 22 12:42 EST 2020. Contains 332136 sequences. (Running on oeis4.)