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.

A017934 Powers of sqrt(10) rounded down.

Original entry on oeis.org

1, 3, 10, 31, 100, 316, 1000, 3162, 10000, 31622, 100000, 316227, 1000000, 3162277, 10000000, 31622776, 100000000, 316227766, 1000000000, 3162277660, 10000000000, 31622776601, 100000000000, 316227766016, 1000000000000, 3162277660168, 10000000000000
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010467 Decimal expansion of sqrt(10), A131581, A136582, A175733, A175734.

Programs

Formula

a(n) = floor(sqrt(10^n)). - Zak Seidov

A132153 Largest prime <= square root of 10^n.

Original entry on oeis.org

3, 7, 31, 97, 313, 997, 3137, 9973, 31607, 99991, 316223, 999983, 3162277, 9999991, 31622743, 99999989, 316227731, 999999937, 3162277633, 9999999967, 31622776589, 99999999977, 316227766003, 999999999989, 3162277660153, 9999999999971, 31622776601657
Offset: 1

Views

Author

Anthony C Robin, Nov 01 2007

Keywords

Comments

To check if an (n+1)-digit number is prime, a(n) is the largest prime which one needs to check is not a factor of the (n+1)-th digit number. For example, to check that a general four-digit number is not prime, we need to test its divisibility by all the primes up to and including 97.

Links

Crossrefs

Cf. A017934, A131581, A136582, A175733, A175734.
Cf. A000040, A122121, A003618.

Programs

  • Mathematica
    Table[NextPrime[Sqrt[10^n],-1],{n,27}] (* James C. McMahon, Mar 04 2025 *)
  • PARI
    a(n)=precprime(sqrtint(10^n)) \\ Charles R Greathouse IV, Aug 18 2011
  • Python
    from sympy import prevprime, integer_nthroot
def a(n): return prevprime(integer_nthroot(10**n, 2)[0]+1)
print([a(n) for n in range(1, 28)]) # Michael S. Branicky, Dec 23 2021

Formula

a(n) = A000040(A122121(n)). a(2n) = A003618(n). - R. J. Mathar, Nov 06 2007 [Corrected by Jaroslav Krizek, Jul 12 2010]
a(n) = sqrt(A175734(n)). - Jaroslav Krizek, Aug 24 2010

Extensions

More terms from N. J. A. Sloane, Jan 05 2008

A131581 The next prime greater than the square root of 10^n.

Original entry on oeis.org

2, 5, 11, 37, 101, 317, 1009, 3163, 10007, 31627, 100003, 316241, 1000003, 3162283, 10000019, 31622777, 100000007, 316227767, 1000000007, 3162277669, 10000000019, 31622776621, 100000000003, 316227766069, 1000000000039
Offset: 0

Views

Author

Robert G. Wilson v, Jan 12 2007

Keywords

Comments

The difference between a(n) and floor(sqrt(10^n)): 1, 2, 1, 6, 1, 1, 9, 1, 7, 5, 3, 14, 3, 6, 19, 1, 7, 1, 7, 9, ....
Values for which the difference between a(n) and floor(sqrt(10^n)) equals one: 0, 2, 4, 5, 7, 15, 17, 25, 145, 1079, ..., (1350). Only even terms are 0, 2 & 4; all the rest must be odd.

Crossrefs

Cf. A003617, A132153, A136582, A175733, A175734.

Programs

  • Mathematica
    NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Table[ NextPrim@ Floor@ Sqrt[10^n], {n, 0, 25}]
Table[NextPrime[Sqrt[10^n]],{n,0,30}] (* Harvey P. Dale, Aug 15 2017 *)

Formula

a(n) = sqrt(A175733(n+1)). [From Jaroslav Krizek, Aug 24 2010]

A136582 Sqrt(10)-primes: primes obtained by concatenating the first digits in the decimal expansion of sqrt(10).

Original entry on oeis.org

3, 31, 3162277, 316227766016837933, 316227766016837933199889354443271
Offset: 1

Views

Author

Lekraj Beedassy, Jan 09 2008

Keywords

Comments

n such that floor(sqrt(10^(2*n-1))) is prime (1, 2, 7, 18, 33, ...) are given in A136583.
This sequence is the list of prime terms in A017934.
The next term has 206 digits. - Harvey P. Dale, Dec 06 2023

Crossrefs

Cf. A010467, A017934, A017934, A131581, A132153, A136583, A175733, A175734.

Programs

  • Magma
    // by Jason Kimberley, Aug 2011
for n in [1..499 by 2] do
  f := Isqrt(10^n);
  if IsPrime(f) then
    printf "%o,", f;
  end if;
end for;
  • Mathematica
    Module[{nn=50,sq10},sq10=RealDigits[Sqrt[10],10,nn][[1]];Select[FromDigits/@Table[Take[sq10,n],{n,nn}],PrimeQ]] (* Harvey P. Dale, Dec 06 2023 *)

Formula

a(n) = A017934(2*A136583(n)-1).

A175733 a(n) is the smallest n-digit number with 3 divisors.

Original entry on oeis.org

4, 25, 121, 1369, 10201, 100489, 1018081, 10004569, 100140049, 1000267129, 10000600009, 100008370081, 1000006000009, 10000033772089, 100000380000361, 1000000025191729, 10000001400000049, 100000000621806289, 1000000014000000049, 10000000055856073561
Offset: 1

Views

Author

Jaroslav Krizek, Aug 24 2010

Keywords

Crossrefs

Cf. A131581, A132153, A136582, A175734.

Programs

  • Mathematica
    Table[Prime[1 + PrimePi[Sqrt[10^n]]]^2, {n, 0, 25}] (* T. D. Noe, Aug 19 2011 *)
  • Python
    from math import sqrt
from sympy import nextprime
def a(n): return nextprime(int(sqrt(10**n+1)))**2
print([a(n) for n in range(20)]) # Michael S. Branicky, Apr 25 2021

Formula

a(n) = A131581(n-1)^2.

A136583 n such that floor(sqrt(10^(2*n-1))) is (probably) prime.

Original entry on oeis.org

1, 2, 7, 18, 33, 206, 468, 1061, 6831, 40377
Offset: 1

Views

Author

Lekraj Beedassy, Jan 09 2008

Keywords

Comments

Number of digits of sqrt(10)-primes (A136582).
The n such that A017934(2*n-1) is (probably) prime.

Crossrefs

Cf. A010467, A017934, A017934, A131581, A132153, A136582, A175733, A175734.

Programs

  • Magma
    for n in [1..10^6] do if IsPrime(Isqrt(10^(2*n-1))) then printf "%o, ", n; end if; end for; // Jason Kimberley, Sep 03 2011
  • Mathematica
    rd = RealDigits[Sqrt[10], 10, 10^5][[1]]; Do[ If[ PrimeQ@ FromDigits@ Take[rd, n], Print@n], {n, 10^5}] (* Robert G. Wilson v, Jan 20 2008 *)

Extensions

a(6) - a(8) from Robert G. Wilson v, Jan 20 2008
Probable terms a(9) and a(10) from Jason Kimberley, Aug 19 and Sep 03 2011
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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