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

Author

Ilya Gutkovskiy, Jan 13 2016

Keywords

• nonn
• easy
• base

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..995
• Eric Weisstein's World of Mathematics, Pythagoras's Constant.

Crossrefs

Cf. A002193, A081368, A090897, A093473.

Programs

Magma

[Floor(Sqrt(2)*10^(n*(n + 1)/2 - 1)) mod (10^n): n in [1..30]]; // Vincenzo Librandi, Feb 15 2016

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 *)

PARI

a(n) = lift(Mod(floor(sqrt(2)*10^(n*(n + 1)/2 - 1)), 10^n)); \\ G. C. Greubel, Oct 07 2018

Formula

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