cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A283158 Numbers k such that A011544(k-1) is a prime.

Original entry on oeis.org

1, 85, 555, 1508, 1781, 4224, 7037, 43740
Offset: 1

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Author

XU Pingya, Mar 01 2017

Keywords

Comments

For k <= 16000, there are seven primes in sequence A011544.
Round(e*10^112279) = floor(e*10^112279), and floor(e*10^112279) = A011544(112279) (=A007512(7)) is a prime. Thus 112280 = A064118(7) is also a term.

Crossrefs

Programs

  • Mathematica
    Do[If[PrimeQ[Round[E*10^(n-1)]],Print[n]],{n,16000}]

Extensions

a(2) = 85 added by Jason Yuen, Jun 16 2025
a(8) from Michael S. Branicky, Jun 24 2025

A011546 Decimal expansion of Pi rounded to n places.

Original entry on oeis.org

3, 31, 314, 3142, 31416, 314159, 3141593, 31415927, 314159265, 3141592654, 31415926536, 314159265359, 3141592653590, 31415926535898, 314159265358979, 3141592653589793, 31415926535897932, 314159265358979324, 3141592653589793238, 31415926535897932385, 314159265358979323846
Offset: 0

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Author

Keywords

Comments

Scherzer (2012) writes: "The 17th-most common 10-digit password is 3141592654 (for you non-math nerds, those are the first [ten] digits of Pi)." The information comes from an analysis of expired ATM PIN codes conducted by Nick Berry of Data Genetics. - Alonso del Arte, Sep 21 2012

Examples

			a(4) = floor(10^4 * Pi + 0.5) = 31416.
		

Crossrefs

Programs

  • Maple
    a:= proc(n) Digits:= n+20;
           round(10^n * Pi)
        end:
    seq(a(n), n=0..20); # Alois P. Heinz, Mar 11 2016
  • Mathematica
    Module[{nn=20,pid},pid=RealDigits[Pi,10,nn+2][[1]];Table[Floor[ (FromDigits[ Take[pid,n+1]])/10+1/2],{n,nn}]] (* Harvey P. Dale, Oct 09 2017 *)
    Round[Pi*10^Range[0, 20]] (* Paolo Xausa, Jul 08 2025 *)
  • PARI
    a(n)=round(Pi*10^n) \\ Charles R Greathouse IV, Sep 21 2012

Formula

a(n) = floor(10^n * Pi + 0.5).

A011543 Decimal expansion of e truncated to n places.

Original entry on oeis.org

2, 27, 271, 2718, 27182, 271828, 2718281, 27182818, 271828182, 2718281828, 27182818284, 271828182845, 2718281828459, 27182818284590, 271828182845904, 2718281828459045, 27182818284590452, 271828182845904523, 2718281828459045235, 27182818284590452353, 271828182845904523536
Offset: 0

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Author

Keywords

Comments

a(n) <= A011544(n) <= a(n)+1. - Danny Rorabaugh, Mar 07 2015

Crossrefs

Programs

  • Mathematica
    Module[{nn=30,edgs},edgs=RealDigits[E,10,nn][[1]];Table[ FromDigits[ Take[ edgs, n]],{n,nn}]] (* Harvey P. Dale, Oct 04 2017 *)
  • PARI
    a(n) = floor(exp(1)*10^n); \\ Michel Marcus, Mar 08 2015
    
  • Python
    from sympy import E
    def a(n): return int(E*10**n)
    print([a(n) for n in range(21)]) # Michael S. Branicky, Feb 27 2021

Formula

a(n) = floor(e*10^n).

A011548 Decimal expansion of sqrt(2) rounded to n places.

Original entry on oeis.org

1, 14, 141, 1414, 14142, 141421, 1414214, 14142136, 141421356, 1414213562, 14142135624, 141421356237, 1414213562373, 14142135623731, 141421356237310, 1414213562373095, 14142135623730950, 141421356237309505, 1414213562373095049, 14142135623730950488, 141421356237309504880
Offset: 0

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Keywords

References

  • W. Rudin, Principles of Mathematical Analysis, 3rd ed., McGraw-Hill, 1976.

Crossrefs

Programs

  • Mathematica
    Round[Table[N[Sqrt[2], k] 10^(k - 1), {k, 20}]] (* Vincenzo Librandi, Aug 17 2013 *)
    Module[{nn=20,s},s=RealDigits[Sqrt[2],10,nn+1][[1]];Table[Round[ FromDigits[ Take[ s,n+1]]/10],{n,nn}]] (* Harvey P. Dale, Apr 04 2019 *)
  • Python
    from math import isqrt
    def A011548(n): return (m:=isqrt(k:=10**(n<<1)<<1))+int((k-m*(m+1)<<2)>=1) # Chai Wah Wu, Jul 29 2022

A011552 Decimal expansion of phi rounded to n places.

Original entry on oeis.org

2, 16, 162, 1618, 16180, 161803, 1618034, 16180340, 161803399, 1618033989, 16180339887, 161803398875, 1618033988750, 16180339887499, 161803398874989, 1618033988749895, 16180339887498948, 161803398874989485, 1618033988749894848, 16180339887498948482, 161803398874989484820
Offset: 0

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Keywords

Crossrefs

Programs

  • Mathematica
    Round[GoldenRatio*10^Range[0, 20]] (* Paolo Xausa, May 02 2024 *)

Extensions

More terms from Paolo Xausa, Jul 08 2025

A085830 Least number k such that (10^n)^k < k!.

Original entry on oeis.org

2, 25, 269, 2714, 27177, 271822, 2718274, 27182809, 271828173, 2718281817, 27182818272, 271828182832, 2718281828444, 27182818284575, 271828182845887, 2718281828459027, 27182818284590433, 271828182845904503
Offset: 0

Views

Author

Robert G. Wilson v, Jul 13 2003

Keywords

Comments

A085830(n) = A065027(10^n). This should confirm that the lim n -> infinity of A065027(n)/n -> e from below.
a(63) differs from the Floor(10^63* e) by only 33.

Crossrefs

Programs

  • Mathematica
    LogBaseBStirling[b_, n_] := Block[{}, N[ Log[b, 2*Pi*n]/2 + n*Log[b, n/E] + Log[b, 1 + 1/(12n) + 1/(288n^2) - 139/(51840n^3) - 571/(2488320n^4) + 163879/(209018880n^5)], 64]]; f[0] = 2; f[n_] := f[n] = Block[{k = 10*g[n - 1]}, While[ LogBaseBStirling[10^n, k] <= k, k++ ]; k]; Table[ f[n], {n, 1, 18}]
Showing 1-6 of 6 results.