A001672 -id:A001672 - cp's OEIS frontend

A117882 Partial sums of floor(Pi^n).

1, 4, 13, 44, 141, 447, 1408, 4428, 13916, 43725, 137373, 431577, 1355846, 4259523, 13381694, 42039839, 132072059, 414916622, 1303499025, 4095062974, 12865019770, 40416651612, 126972655803, 398896362696, 1253169882609

Offset: 0

Jonathan Vos Post, May 02 2006

The only prime in the sequence through a(50) is a(2) = 13.

Cf. A001672.

Accumulate[Table[Floor[\[Pi]^n],{n,0,30}]]  (* Harvey P. Dale, Apr 21 2011 *)

a(n) = Sum_{i=0..n} A001672(i).

a(n) = Sum_{i=0..n} floor(Pi^i).

A140471 Floored n-th power of Viswanath's constant.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 22, 25, 28, 32, 36, 41, 46, 52, 59, 67, 76, 86, 98, 111, 125, 142, 161, 182, 206, 233, 264, 299, 339, 384, 434, 492, 557, 630, 713, 808, 914, 1035, 1172, 1326, 1502, 1700, 1924

Offset: 0

Alonso del Arte, Jun 28 2008

nonn

For sufficiently large terms of a random Fibonacci sequence, the powers of Viswanath's constant approximate the absolute value of the terms in such a sequence (with a few notable exceptions).

			a(7) = 2 because V^7 is approximately 2.381734947432 and floored that is 2.

Eric Weisstein, Random Fibonacci sequence at MathWorld

Cf. A014217, floored n-th power of the golden ratio; A000149, floored n-th power of e; A001672, floored n-th power of Pi.

V = 1.1319882487943; Table[Floor[V^n], {n, 0, 49}]

a(n) = floor(v^n), where v = 1.1319882487943 as given by A078416.

More terms from Alois P. Heinz, Mar 08 2020

A247168 Number of times n occurs in the sequence floor(log_Pi(i)) with i=1,2,3,... .

Original entry on oeis.org

6, 22, 66, 209, 655, 2059, 6468, 20321, 63839, 200556, 630065, 1979408, 6218494, 19535974, 61374075, 192812343, 605737840, 1902981546, 5978392847, 18781675046, 59004372349, 185367702702, 582349813020, 1829505894404, 5747562277559, 18056499427227

Offset: 1

Talha Ali, Nov 29 2014

nonn

Cf. A000796, A001672.

a(n) = floor(Pi^(n+1)) - floor(Pi^(n)) = A001672(n+1) - A001672(n), n>=1.

A309946 a(n) = floor(Pi^n/Zeta(n)).

Original entry on oeis.org

0, 6, 25, 90, 295, 945, 2995, 9450, 29749, 93555, 294058, 924041, 2903320, 9121612, 28657269, 90030844, 282842403, 888579011, 2791558622, 8769948429, 27551618702, 86555983552, 271923674474, 854273468992, 2683779334331, 8431341566236, 26487840921750, 83214006759229, 261424512797515

Offset: 1

Seiichi Manyama, Aug 24 2019

nonn

			Pi^12/Zeta(12) = 638512875/691 = 924041.78... So a(12) = 924041.

Index entries for zeta function.

Decimal expansion of Pi^k/Zeta(k): A308637 (k = 3), A309926 (k = 5), A309927 (k = 7), A309928 (k = 9), A309929 (k = 11).

Cf. A001672 (floor(Pi^n)), A002432, A046988, A100594.

Table[Floor[Pi^n/Zeta[n]], {n, 20}] (* Alonso del Arte, Aug 24 2019 *)

{a(n) = if(n==1, 0, n==4, 90, floor(Pi^n/zeta(n)))}

a(2*n) = A100594(n).

cp's OEIS Frontend

A117882 Partial sums of floor(Pi^n).

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A140471 Floored n-th power of Viswanath's constant.

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A247168 Number of times n occurs in the sequence floor(log_Pi(i)) with i=1,2,3,... .

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A309946 a(n) = floor(Pi^n/Zeta(n)).

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