A104103 -id:A104103 - cp's OEIS frontend

A145445 a(n) = the smallest square > n-th prime.

4, 4, 9, 9, 16, 16, 25, 25, 25, 36, 36, 49, 49, 49, 49, 64, 64, 64, 81, 81, 81, 81, 100, 100, 100, 121, 121, 121, 121, 121, 144, 144, 144, 144, 169, 169, 169, 169, 169, 196, 196, 196, 196, 196, 225, 225, 225, 225, 256, 256, 256, 256, 256, 256, 289, 289, 289, 289

Offset: 1

Zak Seidov, Oct 10 2008

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A104103.

Cf. A000040, A000290, A014085 (run lengths), A245508.

a145445 n = a145445_list !! (n-1)
a145445_list = f a000040_list $ drop 2 a000290_list where
   f ps'@ (p:ps) xs'@(x:xs) = if p < x then x : f ps xs' else f ps' xs
-- Reinhard Zumkeller, Jul 25 2014

Table[Ceiling[Prime[n]^(1/2)]^2,{n,100}]

from sympy import prime, integer_nthroot
def a(n): return (integer_nthroot(prime(n), 2)[0]+1)**2
print([a(n) for n in range(1, 59)]) # Michael S. Branicky, Apr 04 2021

a(n) = A104103(n)^2.

A103416 a(n) = n - ceiling(sqrt(prime(n))).

Original entry on oeis.org

-1, 0, 0, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 8, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 15, 16, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 25, 26, 26, 27, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 44, 44, 45, 46, 47, 48, 48, 49, 50, 51, 52, 53, 53, 54, 55

Offset: 0

Giovanni Teofilatto, Mar 21 2005

sign

Cf. A104103.

Table[n - Ceiling[ Sqrt[ Prime[ n]]], {n, 75}] (* Robert G. Wilson v, Mar 24 2005 *)

from math import isqrt
from sympy import prime
def A103416(n): return n-isqrt(prime(n+1)) # Chai Wah Wu, Jul 29 2022

a(n) = n - A104103(n). - Michel Marcus, Jul 30 2022

More terms from Robert G. Wilson v, Mar 24 2005

A145447 a(n) = the smallest square (and/or cube) > n-th prime.

Original entry on oeis.org

4, 4, 8, 8, 16, 16, 25, 25, 25, 36, 36, 49, 49, 49, 49, 64, 64, 64, 81, 81, 81, 81, 100, 100, 100, 121, 121, 121, 121, 121, 144, 144, 144, 144, 169, 169, 169, 169, 169, 196, 196, 196, 196, 196, 216, 216, 216, 225, 256, 256, 256, 256, 256, 256, 289, 289, 289, 289

Offset: 1

Zak Seidov, Oct 10 2008

nonn

a(n) = min(A145445(n), A145446(n) )= min ([A104103(n)]^2, [A104147(n)]^3)

A104103, A104147, A145445, A145446

Table[Min[{Ceiling[Prime[n]^(1/3)]^3,Ceiling[Prime[n]^(1/2)]^2}],{n,100}]

A145449 Numbers n such that A145445(n) = A145446(n).

Original entry on oeis.org

16, 17, 18, 123, 124, 125, 126, 127, 128, 129, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 1797, 1798, 1799, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818

Offset: 1

Zak Seidov, Oct 10 2008

nonn

Numbers n such that s(n), the smallest square > n-th prime, equals q(n), the smallest cube > n-th prime, s(n) = A145445(n), q(n) = A145446(n).

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

A104103, A104147, A145445, A145446, A145447

Do[If[Ceiling[Prime[n]^(1/3)]^3 == Ceiling[Prime[n]^(1/2)]^2,Print[n]],{n,10000}]

A166127 Minimum value of j such that floor(j^2 / prime(n)) > 0.

Original entry on oeis.org

0, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20

Offset: 1

Christopher Hunt Gribble, Oct 07 2009

nonn

Essentially the same as A104103. - R. J. Mathar, Jul 21 2015

C. H. Gribble, Table of n, a(n) for n=1,..., 78498 (i.e. for primes < 10^6).

Cf. A165974

Join[{0},Table[Ceiling[Sqrt[p]],{p,Prime[Range[2,80]]}]] (* Harvey P. Dale, Oct 10 2020 *)

A123241 Number of squares < lesser of twin primes.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 12, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 21, 21, 22, 23, 24, 25, 25, 26, 26, 29, 29, 29, 30, 30, 32, 33, 33, 33, 34, 34, 36, 36, 36, 37, 37, 38, 39, 39, 39, 41, 41, 41, 42, 42, 43, 44, 44, 44, 45, 45, 46, 46, 46, 46, 47, 47, 48, 48, 49, 49, 49

Offset: 1

Giovanni Teofilatto, Oct 07 2006

Cf. A104103 number of squares < prime(n).

ltp=Select[Prime[Range[PrimePi[2500]]],PrimeQ[#+2]&];Ceiling[Sqrt[ltp]] (* James C. McMahon, Nov 17 2024 *)

a(n)=A003059(A001359(n)). - R. J. Mathar, Jun 18 2008

More terms from R. J. Mathar, Jun 18 2008

cp's OEIS Frontend

A145445 a(n) = the smallest square > n-th prime.

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A103416 a(n) = n - ceiling(sqrt(prime(n))).

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A145447 a(n) = the smallest square (and/or cube) > n-th prime.

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Mathematica

A145449 Numbers n such that A145445(n) = A145446(n).

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Programs

Mathematica

A166127 Minimum value of j such that floor(j^2 / prime(n)) > 0.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A123241 Number of squares < lesser of twin primes.

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Author

Keywords

Crossrefs

Programs

Mathematica

Formula

Extensions