A048761 -id:A048761 - cp's OEIS frontend

A267032 Difference between smallest integer square >= 10^(2n+1) and 10^(2n+1).

6, 24, 489, 4569, 14129, 147984, 2149284, 25191729, 621806289, 5259630921, 19998666404, 102500044289, 3925449108561, 13071591635856, 42248099518244, 4224809951824400, 43007675962234436, 506034404021388356, 6997839444766224, 699783944476622400

Offset: 0

Gwillim Law, Jan 09 2016

nonn

			a(0) = 6 = 4^2 - 10; a(1) = 24 = 32^2 - 1000.

Robert Israel, Table of n, a(n) for n = 0..998
Gwillim Law, blog post, Dec. 12, 2015

Cf. A048761, A068527.

Cf. A238454 (a similar sequence with powers of 2). - Michel Marcus, Jan 17 2016

f:= proc(n) local s;
  s:= isqrt(10^(2*n+1));
  if s^2 < 10^(2*n+1) then s:= s+1 fi;
  s^2 - 10^(2*n+1)
end proc:
seq(f(n),n=0..40); # Robert Israel, Jan 17 2016

dsis[n_]:=Module[{c=10^(2n+1)},(Floor[Sqrt[c]]+1)^2-c]; Array[dsis,20,0] (* Harvey P. Dale, Apr 27 2019 *)

from math import isqrt
def A267032(n): return (isqrt(m:=10**((n<<1)+1))+1)**2-m # Chai Wah Wu, Apr 27 2023

a(n) = A068527(A013715(n)). - Michel Marcus, Jan 17 2016

A076621 Least square greater than the product of two successive primes.

Original entry on oeis.org

9, 16, 36, 81, 144, 225, 324, 441, 676, 900, 1156, 1521, 1764, 2025, 2500, 3136, 3600, 4096, 4761, 5184, 5776, 6561, 7396, 8649, 9801, 10404, 11025, 11664, 12321, 14400, 16641, 17956, 19044, 20736, 22500, 23716, 25600, 27225, 28900, 30976, 32400, 34596, 36864

Offset: 1

Reinhard Zumkeller, Oct 22 2002

nonn

Cf. A006094, A048761, A074927.

Ceiling[Sqrt[Times@@#]]^2&/@Partition[Prime[Range[50]],2,1] (* Harvey P. Dale, Aug 26 2013 *)

from sympy import prime, primerange
def aupton(terms):
    primes = list(primerange(3, prime(terms+1)+1))
    return [9] + [((p+q)//2)**2 for p, q in zip(primes[:-1], primes[1:])]
print(aupton(43)) # Michael S. Branicky, Sep 16 2021

a(n) = A048761(A006094(n)).
a(n) = prime(n)*prime(n+1)+((prime(n)-prime(n+1))/2)^2 = A006094(n) + A074927(n) for n > 1.
a(n) = ((prime(n)+prime(n+1))/2)^2 for n > 1.

cp's OEIS Frontend

A267032 Difference between smallest integer square >= 10^(2n+1) and 10^(2n+1).

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A076621 Least square greater than the product of two successive primes.

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Formula

cp's OEIS Frontend

A267032 Difference between smallest integer square >= 10^(2*n+1) and 10^(2*n+1).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Python

Formula

A076621 Least square greater than the product of two successive primes.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Python

Formula

A267032 Difference between smallest integer square >= 10^(2n+1) and 10^(2n+1).