A049716 -id:A049716 - cp's OEIS frontend

A049711 a(n) = n - prevprime(n).

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

Offset: 3

N. J. A. Sloane

nonn

All runs end in even numbers at a(p), new highs are found at A000101 and the increasing gap size is A005250. - Robert G. Wilson v, Dec 07 2001

All terms are positive since here the variant 2 (A151799(n) < n) of the prevprime function is used, rather than the variant 1 (A007917(n) <= n). - M. F. Hasler, Sep 09 2015

Cf. A000101, A005250, A049613, A049653, A049716, A049847, A064722.
Cf. A151799, A007917.
Cf. A175851.

Maple
```
A049711 := n-> n-prevprime(n);
```

PrevPrim[n_] := Block[ {k = n - 1}, While[ !PrimeQ[k], k-- ]; Return[k]]; Table[ n - PrevPrim[n], {n, 3, 100} ]
Array[#-NextPrime[#,-1]&,100,3] (* Harvey P. Dale, Dec 07 2011 *)

A049711(n)=n-precprime(n-1) \\ M. F. Hasler, Sep 09 2015

a(n) = A064722(n-1) + 1. - Pontus von Brömssen, Jul 31 2022

A049653 a(n) = 2n - prevprime(2n).

Original entry on oeis.org

1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 3, 5, 1, 1, 3, 5, 1, 3, 1, 1, 3, 1, 3, 5, 1, 3, 5, 1, 1, 3, 5, 1, 3, 1, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 7, 1, 3, 1, 1, 3, 1, 1, 3, 1, 3, 5, 7, 9, 11, 13, 1, 3, 1, 3, 5, 1, 1, 3, 5, 7, 9, 1, 1, 3, 5, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 1, 1, 3, 5, 7

Offset: 2

N. J. A. Sloane

nonn

G. C. Greubel, Table of n, a(n) for n = 2..5000

Cf. A049613, A049711, A049716, A049847.

[2*n - NthPrime(#PrimesUpTo(2*n)): n in [2..50]]; // G. C. Greubel, Dec 05 2017

Table[2*n - NextPrime[2*n, -1], {n, 2, 50}] (* G. C. Greubel, Dec 05 2017 *)

for(n=2,50, print1(2*n - precprime(2*n), ", ")) \\ G. C. Greubel, Dec 05 2017

a(n) = A049711(2*n). - R. J. Mathar, Oct 26 2015

A049613 a(n) = 2n - (largest prime < 2n-2).

Original entry on oeis.org

3, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 7, 3, 3, 5, 7, 3, 5, 3, 3, 5, 3, 5, 7, 3, 5, 7, 3, 3, 5, 7, 3, 5, 3, 3, 5, 7, 3, 5, 3, 5, 7, 3, 5, 7, 9, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 7, 9, 11, 13, 15, 3, 5, 3, 5, 7, 3, 3, 5, 7, 9, 11, 3, 3, 5, 7, 3, 5, 7, 3, 5, 3, 5, 7, 3, 5, 7, 3, 3, 5

Offset: 3

David M. Elder (elddm(AT)rhodes.edu)

			a(14)=28 - (largest prime < 26) = 28 - 23 = 5.

T. D. Noe, Table of n, a(n) for n=3..10000

Cf. A049653, A049711, A049716, A049847.

Cf. A002373, A020481, A007917.

a049613 n = 2 * n - a007917 (2 * n - 2)
-- Reinhard Zumkeller, Jan 02 2015

Table[2n-NextPrime[2n-2,-1],{n,3,100}] (* Harvey P. Dale, Aug 16 2011 *)

a(n) <= A002373(n). - R. J. Mathar, Mar 19 2008

a(n) = 2*n - A007917(2*n-2). - Reinhard Zumkeller, Jan 02 2015

A049847 a(n) = (2n + 1 - prevprime(2n+1))/2.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 3, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 4, 5, 6, 7, 1, 2, 1, 2, 3, 1, 1, 2, 3, 4, 5, 1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 1, 2, 3, 4

Offset: 2

N. J. A. Sloane

nonn

Cf. A049613, A049653, A049711, A049716.

Table[(2n+1-NextPrime[2n+1,-1])/2,{n,2,100}] (* Harvey P. Dale, Jul 25 2015 *)

cp's OEIS Frontend

A049711 a(n) = n - prevprime(n).

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Maple

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A049653 a(n) = 2*n - prevprime(2*n).

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Magma

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A049613 a(n) = 2n - (largest prime < 2n-2).

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Haskell

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A049847 a(n) = (2*n + 1 - prevprime(2*n+1))/2.

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Mathematica

A049653 a(n) = 2n - prevprime(2n).

A049847 a(n) = (2n + 1 - prevprime(2n+1))/2.