A049847 -id:A049847 - 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

A049716 a(n) = 2n + 1 - prevprime(2n + 1).

Original entry on oeis.org

1, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 4, 6, 2, 2, 4, 6, 2, 4, 2, 2, 4, 2, 4, 6, 2, 4, 6, 2, 2, 4, 6, 2, 4, 2, 2, 4, 6, 2, 4, 2, 4, 6, 2, 4, 6, 8, 2, 4, 2, 2, 4, 2, 2, 4, 2, 4, 6, 8, 10, 12, 14, 2, 4, 2, 4, 6, 2, 2, 4, 6, 8, 10, 2, 2, 4, 6, 2, 4, 6, 2, 4, 2, 4, 6, 2, 4, 6, 2, 2, 4

Offset: 1

N. J. A. Sloane

nonn

			n:     1  2  3  4  5  6  7  8 ...
2n+1:  3  5  7  9 11 13 15 17 ...
pp:    2  3  5  7  7 11 13 13 ...
diff:  1  2  2  2  4  2  2  4 ...

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A049613, A049653, A049711, A049847.

seq(2*n+1-prevprime(2*n+1), n=1..100); # Robert Israel, Jul 05 2018

Table[2n+1-NextPrime[2n+1,-1],{n,100}] (* Harvey P. Dale, Sep 21 2013 *)

a(n) = 2*n+1-precprime(2*n); \\ Michel Marcus, Jul 06 2018

a(n) = A049711(2*n+1). - R. J. Mathar, Oct 26 2015

A255274 From Goldbach conjecture: Consider the pairs (2n-+1, 3), (2n-1, 5), (2n-3, 7), ..., (3, 2n+1) of odd numbers having sum 2n+4; a(n) is the index of the first pair of primes (p, q) on the list.

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, 9, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 6, 5, 6, 9, 1, 2, 1, 2, 3, 1, 1, 2, 3, 5, 5, 1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2

Offset: 1

Michel Lagneau, Feb 20 2015

nonn

a(n) = A049847(n) for n = 1..46. The values of n such that a(n) is different from A049847(n) are 47, 59, 62, 72, 93, 102, 108, 123, 144, 149, 152, 161, 164, 171, 182, 197, 203, 207, 213, 227, ...

The corresponding pairs of primes are (3, 3), (3, 5), (3, 7), (5, 7), (3, 11), (3, 13), (5, 13), (3, 17), ... (A210957).

			a(13)=3 because 2*13 + 4 = 30 => 13 pairs (27,3), (25,5), (23,7), ..., (3,27) and the pair (23,7) is the third pair having prime elements.

Michel Lagneau, Table of n, a(n) for n = 1..10000
Jon Maiga, Computer-generated formulas for A255274, Sequence Machine.

Cf. A000040, A002375, A049847, A210957, A020482.

nn:=100:for n from 6 by 2 to nn do:ii:=0:it:=1:for p from 3 by 2 to n while(ii=0) do:if type(n-p,prime)=true and type(p,prime)=true then ii:=1: printf(`%d, `,it):else it:=it+1:fi:od:od:

a(n)=my(m=2*n+4); forprime(q=3, n+2, if(isprime(m-q), return(q\2))) \\ Charles R Greathouse IV, Jan 07 2022

a(n) = n + (3-A020482(n+2))/2 = (A020481(n+2)-1)/2 via the Maiga link. - Bill McEachen, Jan 02 2022

Edited by N. J. A. Sloane, Sep 12 2017

cp's OEIS Frontend

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

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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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A049716 a(n) = 2*n + 1 - prevprime(2*n + 1).

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A255274 From Goldbach conjecture: Consider the pairs (2n-+1, 3), (2n-1, 5), (2n-3, 7), ..., (3, 2n+1) of odd numbers having sum 2n+4; a(n) is the index of the first pair of primes (p, q) on the list.

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Maple

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Formula

Extensions

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

A049716 a(n) = 2n + 1 - prevprime(2n + 1).