A072680 -id:A072680 - cp's OEIS frontend

A072681 a(n) = (n - A007917(n)) * (A007918(n) - n).

0, 0, 1, 0, 1, 0, 3, 4, 3, 0, 1, 0, 3, 4, 3, 0, 1, 0, 3, 4, 3, 0, 5, 8, 9, 8, 5, 0, 1, 0, 5, 8, 9, 8, 5, 0, 3, 4, 3, 0, 1, 0, 3, 4, 3, 0, 5, 8, 9, 8, 5, 0, 5, 8, 9, 8, 5, 0, 1, 0, 5, 8, 9, 8, 5, 0, 3, 4, 3, 0, 1, 0, 5, 8, 9, 8, 5, 0, 3, 4, 3, 0, 5, 8, 9, 8, 5, 0, 7, 12, 15, 16, 15, 12, 7, 0, 3, 4, 3, 0, 1, 0

Offset: 2

Reinhard Zumkeller, Jul 01 2002

a(n)=0 iff n is prime.
Local maxima occur at interprimes: a(A024675(n)) = A074927(n+1). - Reinhard Zumkeller, Mar 04 2009
Expanding upon the maxima comment, repetitive subset triplets (like 3,4,3) of form (k,k+1,k) occur when the middle value is a square. - Bill McEachen, Apr 14 2025

Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Cf. A007917, A007918, A007920, A024675, A064722, A072680, A074927.

a[n_] := (n - NextPrime[n+1, -1])*(NextPrime[n] - n); Table[a[n], {n, 2, 103}] (* Jean-François Alcover, Jun 14 2013 *)

a(n) = A064722(n) * A007920(n).

a(n) = A064722(n) * (A072680(n) - A064722(n)).

A097106 a(n) = (Smallest prime power >= n) - (greatest prime power <= n).

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 3, 3, 0, 0, 2, 0, 4, 4, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 5, 5, 5, 5, 0, 4, 4, 4, 0, 2, 0, 4, 4, 4, 0, 2, 0, 4, 4, 4, 0, 6, 6, 6, 6, 6, 0, 2, 0, 3, 3, 0, 3, 3, 0, 4, 4, 4, 0, 2, 0, 6, 6, 6, 6, 6, 0, 2, 0, 2, 0, 6, 6, 6, 6, 6, 0, 8, 8, 8, 8, 8, 8, 8, 0, 4, 4, 4, 0, 2, 0, 4, 4

Offset: 1

Reinhard Zumkeller, Sep 15 2004

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000015, A031218, A000961, A072680.

sp[n_] := If[n == 1, 1, Module[{m = n}, While[!PrimePowerQ[m], m++]; m]];
gp[n_] := If[n == 1, 1, Module[{m = n}, While[!PrimePowerQ[m], m--]; m]];
a[n_] := sp[n] - gp[n];
Array[a, 100] (* Jean-François Alcover, Dec 02 2021 *)

A000015(n) = if(1==n, n, while(!isprimepower(n), n++); n);
A031218(n) = if(1==n, n, while(!isprimepower(n), n--); n);
A097106(n) = (A000015(n) - A031218(n)); \\ Antti Karttunen, Sep 23 2018

a(n) = A000015(n) - A031218(n);

a(n) = 0 iff n is a power of a prime (in A000961).

A329273 a(1)=1. If n is prime, a(n)=0; if not, a(n) = (the smallest prime number greater than n) minus (the largest prime number smaller than n) minus 1.

Original entry on oeis.org

1, 0, 0, 1, 0, 1, 0, 3, 3, 3, 0, 1, 0, 3, 3, 3, 0, 1, 0, 3, 3, 3, 0, 5, 5, 5, 5, 5, 0, 1, 0, 5, 5, 5, 5, 5, 0, 3, 3, 3, 0, 1, 0, 3, 3, 3, 0, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 0, 1, 0, 5, 5, 5, 5, 5, 0, 3, 3, 3, 0, 1, 0, 5, 5, 5, 5, 5, 0, 3, 3, 3, 0, 5, 5, 5, 5, 5, 0, 7, 7, 7, 7, 7, 7, 7, 0, 3, 3, 3

Offset: 1

Todor Szimeonov, Nov 11 2019

nonn

When n is not a prime number, a(n) expresses the size of the prime gap to which n belongs.

			Let n=9. The smallest prime number, greater than 9 is 11, the largest prime number, smaller than 9 is 7. a(9)=11-7-1=3.

Cf. A072680, A151799, A151800.

Array[Which[# == 1, 1, PrimeQ@ #, 0, True, Prime[# + 1] - Prime@ # - 1 &@ PrimePi@ #] &, 105] (* Michael De Vlieger, Nov 18 2019 *)

a(n) = if (n==1, 1, if (isprime(n), 0, nextprime(n+1) - precprime(n-1) - 1)); \\ Michel Marcus, Dec 01 2019

a(1)=1. If n is prime, a(n)=0; if not, a(n) = nextprime(n) - precprime(n) - 1.

The nonzero terms are one less than the nonzero terms of A072680. More precisely, a(n) = A072680(n) - sign(A072680(n)) for n > 1. - Rémy Sigrist, Nov 30 2019

cp's OEIS Frontend

A072681 a(n) = (n - A007917(n)) * (A007918(n) - n).

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A097106 a(n) = (Smallest prime power >= n) - (greatest prime power <= n).

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A329273 a(1)=1. If n is prime, a(n)=0; if not, a(n) = (the smallest prime number greater than n) minus (the largest prime number smaller than n) minus 1.

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