A114761 -id:A114761 - cp's OEIS frontend

A114762 a(n) = floor(3^(1/2)*10^n)^2.

1, 289, 29929, 2999824, 299982400, 29999972025, 2999997202500, 299999997378064, 29999999737806400, 2999999998029351249, 299999999976140205625, 29999999999692481531536, 2999999999996960966074624, 299999999999973224736673344

Offset: 0

Amarnath Murthy, Nov 17 2005

Largest square < 3*10^(2n).

			a(1) = floor(3^(1/2)*10)^2 = 17^2 = 289.

Ivan Panchenko, Table of n, a(n) for n = 0..100

Cf. A114761.

Table[Floor[3^(1/2)*10^n]^2, {n, 0, 20}] (* Stefan Steinerberger, Apr 14 2006 *)
Floor[Sqrt[3] 10^Range[0,20]]^2 (* Harvey P. Dale, Sep 25 2021 *)

More terms from Stefan Steinerberger, Apr 14 2006

A114763 a(n) = floor(sqrt(5)*10^n)^2.

Original entry on oeis.org

4, 484, 49729, 4999696, 499969600, 49999643236, 4999995628489, 499999965341041, 49999999664599209, 4999999997764872529, 499999999955372691076, 49999999999562191467001, 4999999999996468370295001, 499999999999959886546350009, 49999999999999566363399000484

Offset: 0

Amarnath Murthy, Nov 17 2005

nonn

Largest square < 5*10^(2n).

			a(1) = floor(sqrt(5)*10)^2 = 22^2 = 484.

Cf. A114761, A114762.

[Floor(5^(1/2)*10^n)^2: n in [0..150]]; // Vincenzo Librandi, Feb 05 2011

With[{c=Sqrt[5]},(Floor[c 10^#])^2&/@Range[0,30]]  (* Harvey P. Dale, Feb 27 2011 *)

More terms from Joshua Zucker, May 05 2006

A114758 Smallest prime of the form: n successive positive integers in descending order followed by a 1.

Original entry on oeis.org

11, 211, 5431, 76541, 17161514131, 1211109871, 98765431, 876543211, 9876543211, 242322212019181716151, 11109876543211, 1131121111101091081071061051041031021, 555453525150494847464544431

Offset: 1

Amarnath Murthy, Jan 01 2006

			a(4) = 76541, four successive positive integers 7,6,5,4 in descending order followed by a 1.

Robert Israel, Table of n, a(n) for n = 1..173

Cf. A113514, A114754, A114755, A114756, A114757, A114759, A112716, A108145, A114761.

f:= proc(n) local k,p,j;
  for k from 0 do
    p:= parse(cat(seq(k+j,j=n .. 1,-1), 1));
    if isprime(p) then return p fi
  od
end proc:map(f, [$1..15]); # Robert Israel, Apr 03 2023

a[n_]:=(For[m=1, (v={};Do[v=Join[v, IntegerDigits[k]], {k, m+n-1, m, -1}]);!PrimeQ[10FromDigits[v]+1], m++ ];10FromDigits[v]+1);Table[a[n], {n, 14}] (* Farideh Firoozbakht, Jan 02 2006 *)
f[n_] := Block[{t = Reverse@Range@n}, While[p = FromDigits@Flatten@IntegerDigits@Join[t, {1}]; ! PrimeQ@p, t++ ]; p]; Array[f, 13] (* Robert G. Wilson v, Jan 03 2006 *)

Extended by Robert G. Wilson v, Ray Chandler and Farideh Firoozbakht, Jan 02 2006

More terms from Robert G. Wilson v, Jan 03 2006

A114764 a(n) = floor(sqrt(6)*10^n)^2.

Original entry on oeis.org

4, 576, 59536, 5997601, 599956036, 59999522704, 5999996361121, 599999979040609, 59999999863652676, 5999999996163226564, 599999999959251220329, 59999999999844305621284, 5999999999999127500585089, 599999999999961739853364561, 59999999999999603270976352489

Offset: 0

Amarnath Murthy, Nov 17 2005

nonn

Largest square < 6*10^(2n).

			a(1) = floor(sqrt(6)*10)^2 = 24^2 = 576.

Cf. A114761, A114762, A114763.

[Floor(6^(1/2)*10^n)^2: n in [0..150]]; // Vincenzo Librandi, Feb 05 2011

Floor[Sqrt[6] 10^Range[0,20]]^2 (* Harvey P. Dale, Jan 24 2014 *)

More terms from Joshua Zucker, May 05 2006

A114765 a(n) = floor(sqrt(7) * 10^n)^2.

Original entry on oeis.org

4, 676, 69696, 6996025, 699972849, 69999930625, 6999998354001, 699999994145169, 69999999943667161, 6999999999658218721, 699999999965821872100, 69999999999757088783236, 6999999999996874888812096, 699999999999952064012316025, 69999999999999968753591518681

Offset: 0

Amarnath Murthy, Nov 17 2005

nonn

Largest square less than 7 * 10^(2n).

			sqrt(7) = 2.645751311...
floor(sqrt(7) * 10) = 26 and 26^2 = 676, so a(1) = 676.
floor(sqrt(7) * 100) = 264 and 264^2 = 69696, so a(2) = 69696.
floor(sqrt(7) * 1000) = 2645 and 2645^2 = 6996025, so a(3) = 6996025.

Andrew Howroyd, Table of n, a(n) for n = 0..100

Cf. A114761, A114762, A114763, A114764.

Cf. A010465 (sqrt(7)).

[Floor(7^(1/2)*10^n)^2: n in [0..150]]; // Vincenzo Librandi, Feb 05 2011

$MaxExtraPrecision := 200; Table[Floor[7^(1/2) * 10^n]^2, {n, 0, 20}] (* Stefan Steinerberger, Jan 26 2006 *)

a(n)={sqrtint(7*10^(2*n))^2} \\ Andrew Howroyd, Nov 09 2019

More terms from Stefan Steinerberger, Jan 26 2006

Terms a(12) and beyond from Andrew Howroyd, Nov 09 2019

A114766 a(n) = floor(sqrt(8)*10^n)^2.

Original entry on oeis.org

4, 784, 79524, 7997584, 799984656, 79999596964, 7999999294329, 799999986001441, 79999999731514944, 7999999995778911376, 799999999973870935009, 79999999999649835200676, 7999999999998924645564516, 799999999999949033098946521, 79999999999999994478719195161

Offset: 0

Amarnath Murthy, Nov 17 2005

nonn

Largest square < 8*10^(2n).

			a(1) = floor(sqrt(8)*10)^2 = 28^2 = 784.

Cf. A114761, A114762, A114763, A114764, A114765.

[Floor(8^(1/2)*10^n)^2: n in [0..150]]; // Vincenzo Librandi, Feb 04 2011

More terms from Joshua Zucker, May 05 2006

A114767 a(n) = floor(2^(1/3)*10^n)^3.

Original entry on oeis.org

1, 1728, 1953125, 1995616979, 1999899757799, 1999995000191488, 1999999762390486961, 1999999762390486961000, 1999999952878604157540864, 1999999995738432193638080649, 1999999999548194715368954025992, 1999999999976792999366436309113669, 1999999999995841811989967823752208984

Offset: 0

Amarnath Murthy, Nov 17 2005

Largest cube < 2*10^(3n).

			a(1) = floor(2^(1/3)*10)^3 = 1728.

Cf. A114761, A114762, A114763, A114764, A114765, A114766.

With[{c=Power[2, (3)^-1]},Table[(Floor[c 10^n])^3, {n,0,20}]]  (* Harvey P. Dale, Mar 11 2011 *)

More terms from Joshua Zucker, Jan 11 2006

A114768 a(n) = floor(3^(1/3)*10^n)^3.

Original entry on oeis.org

1, 2744, 2985984, 2998442888, 2999690679448, 2999940279271424, 2999996441139764249, 2999999561264112937375, 2999999998081694390995493, 2999999998081694390995493000, 2999999999953769831333566793927, 2999999999953769831333566793927000

Offset: 0

Amarnath Murthy, Nov 17 2005

Largest cube < 3*10^(3*n).

			a(1) = floor(3^(1/3)*10)^3 = 2744.

Cf. A114761, A114762, A114763, A114764, A114765, A114766, A114767.

Table[Floor[3^(1/3)*10^n]^3, {n, 0, 11}] (* Stefan Steinerberger, Mar 24 2006 *)

More terms from Stefan Steinerberger, Mar 24 2006

Missing a(0)=1 inserted by Georg Fischer, Aug 31 2021

A114769 a(n) = floor(4^(1/3)*10^n)^3.

Original entry on oeis.org

1, 3375, 3944312, 3996969003, 3999992047624, 3999992047624000, 3999999607145042201, 3999999607145042201000, 3999999985121344326657625, 3999999992680870612043135651, 3999999999484444277033462628359

Offset: 0

Amarnath Murthy, Nov 17 2005

Largest cube < 4*10^(3n).

			a(1) = floor(4^(1/3)*10)^3 = 3375.

Cf. A114761, A114762, A114763, A114764, A114765, A114766, A114767, A114768.

Table[Floor[4^(1/3)*10^n]^3, {n, 0, 15}] (* Stefan Steinerberger, Mar 26 2006 *)

More terms from Stefan Steinerberger, Mar 26 2006

A114770 a(n) = floor(5^(1/3)*10^n)^3.

Original entry on oeis.org

1, 4913, 4913000, 4991443829, 4999333821299, 4999947835616973, 4999991695706234375, 4999999590549541302479, 4999999941431658940060584, 4999999994063978001557890536, 4999999999327209928022135406696, 4999999999941253653016890923938963, 4999999999993885972304494929654803776

Offset: 0

Amarnath Murthy, Nov 17 2005

Largest cube < 5*10^(3n).

			a(1) = floor(5^(1/3)*10)^3 = 4913.

Cf. A114761, A114762, A114763, A114764, A114765, A114766, A114767, A114768, A114769.

More terms from Joshua Zucker, May 05 2006

cp's OEIS Frontend

A114762 a(n) = floor(3^(1/2)*10^n)^2.

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A114763 a(n) = floor(sqrt(5)*10^n)^2.

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Magma

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A114758 Smallest prime of the form: n successive positive integers in descending order followed by a 1.

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Maple

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A114764 a(n) = floor(sqrt(6)*10^n)^2.

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Magma

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A114765 a(n) = floor(sqrt(7) * 10^n)^2.

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A114766 a(n) = floor(sqrt(8)*10^n)^2.

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Magma

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A114767 a(n) = floor(2^(1/3)*10^n)^3.

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A114768 a(n) = floor(3^(1/3)*10^n)^3.

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