A051700 -id:A051700 - cp's OEIS frontend

A309913 Distance from n to closest squarefree number that is different from n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1

Offset: 0

Ilya Gutkovskiy, Aug 22 2019

nonn

Index entries for sequences related to distance to nearest element of some set

Cf. A005117, A051700, A080733, A316190.

a[n_] := Module[{k = 1}, While[! SquareFreeQ[n + k] && ! SquareFreeQ[n - k], k++]; k]; Table[a[n], {n, 0, 100}]

A341827 a(n) is the distance from n to its more distant neighboring prime.

Original entry on oeis.org

2, 1, 2, 1, 4, 3, 2, 3, 4, 1, 4, 3, 2, 3, 4, 1, 4, 3, 2, 3, 6, 5, 4, 3, 4, 5, 6, 1, 6, 5, 4, 3, 4, 5, 6, 3, 2, 3, 4, 1, 4, 3, 2, 3, 6, 5, 4, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 1, 6, 5, 4, 3, 4, 5, 6, 3, 2, 3, 4, 1, 6, 5, 4, 3, 4, 5, 6, 3, 2, 3, 6, 5, 4, 3, 4, 5, 8

Offset: 3

Ya-Ping Lu, Feb 20 2021

nonn

a(n) is even if n is odd and vice versa. It seems that all records are even.
n - 1 and n + 1 are twin primes if a(n) = 1.
n - 2 and n + 2 are cousin primes for n > 3 if a(n) = 2.
n - 3 and n + 3 are sexy primes if a(n) = A051700(n) = 3.

Cf. A051700, A051698, A077800, A023200, A046132, A023201, A046117.

Array[Max[#1 - #2, #3 - #1] & @@ Prepend[NextPrime[#, {-1, 1}], #] &, 105, 3] (* Michael De Vlieger, Mar 17 2021 *)

for(n=3,88,my(d1=n-precprime(n-1),d2=nextprime(n+1)-n);print1(max(d1,d2),", ")) \\ Hugo Pfoertner, Mar 10 2021

from sympy import prevprime, nextprime
for n in range(3, 1001):
    prevp = prevprime(n); nextp = nextprime(n)
    print(max(n - prevp, nextp - n))

a(n) = max{n - prevprime(n), nextprime(n) - n}.

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A309913 Distance from n to closest squarefree number that is different from n.

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A341827 a(n) is the distance from n to its more distant neighboring prime.

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