A267325 - OEIS

%I #34 Feb 16 2025 08:33:29

%S 1,41,421,3562,37309,504880,1688724,20969807,856967187,5376948073,

%T 17667973799,73247846210,7038850387534,32764157273501,384623091229702,

%U 4924836055850737,21264412149709993,583141322266592750,5592755799950501152,78206057147010955997

%N Next n digits of sqrt(2).

%H G. C. Greubel, <a href="/A267325/b267325.txt">Table of n, a(n) for n = 1..995</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagorassConstant.html">Pythagoras's Constant</a>.

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

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

%t Table[Mod[Floor[Sqrt[2] 10^(n ((n + 1)/2) - 1)], 10^n], {n, 1, 20}]

%t 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}]

%t 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 *)

%o (Magma) [Floor(Sqrt(2)*10^(n*(n + 1)/2 - 1)) mod (10^n): n in [1..30]]; // _Vincenzo Librandi_, Feb 15 2016

%o (PARI) a(n) = lift(Mod(floor(sqrt(2)*10^(n*(n + 1)/2 - 1)), 10^n)); \\ _G. C. Greubel_, Oct 07 2018

%Y Cf. A002193, A081368, A090897, A093473.

%K nonn,easy,base,changed

%O 1,2

%A _Ilya Gutkovskiy_, Jan 13 2016