A267325 Next n digits of sqrt(2).

1, 41, 421, 3562, 37309, 504880, 1688724, 20969807, 856967187, 5376948073, 17667973799, 73247846210, 7038850387534, 32764157273501, 384623091229702, 4924836055850737, 21264412149709993, 583141322266592750, 5592755799950501152, 78206057147010955997

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..995

Eric Weisstein's World of Mathematics, Pythagoras's Constant

Formula

a(n) = floor(sqrt(2)*10^(n*(n + 1)/2 - 1)) mod (10^n).

Example

a(2) = 41 because the second and third digits of sqrt(2) are 4 and 1.

Mathematica

Table[Mod[Floor[Sqrt[2] 10^(n ((n + 1)/2) - 1)], 10^n], {n, 1, 20}]
Table[Floor[10^(-1 + (n (1 + n))/2) Sqrt[2]] + Ceiling[-(Floor[10^(-1 + (n (1 + n))/2) Sqrt[2]]/10^n)] 10^n, {n, 1, 20}]
With[{x=20}, FromDigits/@TakeList[RealDigits[Sqrt[2], 10, (x(x+1))/2] [[1]], Range[x]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 04 2019 *)

Prog

(Magma) [Floor(Sqrt(2)*10^(n*(n + 1)/2 - 1)) mod (10^n): n in [1..30]]; // Vincenzo Librandi, Feb 15 2016
(PARI) a(n) = lift(Mod(floor(sqrt(2)*10^(n*(n + 1)/2 - 1)), 10^n)); \\ G. C. Greubel, Oct 07 2018

Crossrefs

Cf. A002193, A081368, A090897, A093473.

Sequence in context: A068849 A145293 A196807 * A083761 A209823 A196784

Adjacent sequences: A267322 A267323 A267324 * A267326 A267327 A267328

Keyword

nonn,easy,base

Author

Ilya Gutkovskiy, Jan 13 2016

Status

approved