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A171270
a(n) is the only number m such that m = pi(1^(1/n)) + pi(2^(1/n)) + ... + pi(m^(1/n)).
1
3, 11, 33, 95, 273, 791, 2313, 6815, 20193, 60071, 179193, 535535, 1602513, 4799351, 14381673, 43112255, 129271233, 387682631, 1162785753, 3487832975, 10462450353, 31385253911, 94151567433, 282446313695, 847322163873
OFFSET
1,1
COMMENTS
We can easily prove that a(n) = 3^n + 2^n - 2.
FORMULA
a(n) = 3^n + 2^n - 2.
G.f.: x*(3-7*x)/((1-3*x)*(1-2*x)*(1-x)). - Vincenzo Librandi, Mar 03 2014
EXAMPLE
pi(1) + pi(2) + pi(3)=3 so a(1)=3.
MAPLE
A171270:=n->3^n+2^n-2; seq(A171270(n), n=1..30); # Wesley Ivan Hurt, Feb 25 2014
MATHEMATICA
Table[3^n+2^n-2, {n, 26}]
CoefficientList[Series[(3 - 7 x)/((1 - 3 x) (1 - 2 x) (1 - x)), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 03 2014 *)
LinearRecurrence[{6, -11, 6}, {3, 11, 33}, 30] (* Harvey P. Dale, Feb 28 2017 *)
PROG
(PARI) a(n)=3^n+2^n-2 \\ Charles R Greathouse IV, Jun 19 2013
(Magma) [3^n+2^n-2: n in [1..30]]; // Vincenzo Librandi, Mar 03 2014
CROSSREFS
Cf. A000720.
Sequence in context: A288038 A186308 A352102 * A182879 A124640 A081673
KEYWORD
easy,nice,nonn
AUTHOR
Farideh Firoozbakht, May 09 2010
STATUS
approved