A049613 -id:A049613 - 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

A138479 a(n) = smallest prime p such that 2*n + p^2 is another prime, or 0 if no such prime exists.

Original entry on oeis.org

3, 3, 5, 3, 3, 5, 3, 5, 5, 3, 3, 7, 0, 3, 7, 3, 3, 5, 3, 7, 5, 3, 5, 5, 3, 3, 5, 0, 3, 7, 3, 3, 29, 0, 3, 5, 3, 5, 5, 3, 5, 5, 0, 3, 7, 3, 3, 19, 3, 3, 5, 3, 5, 7, 0, 5, 5, 0, 3, 11, 3, 5, 5, 3, 3, 5, 0, 11, 5, 3, 3, 7, 0, 3, 7, 0, 3, 5, 3, 11, 7, 3, 5, 5, 3, 3, 5, 0, 7, 7, 3, 3, 5, 3, 3, 7, 0, 11, 5, 0

Offset: 1

Philippe LALLOUET (philip.lallouet(AT)orange.fr), Mar 20 2008

nonn

For numbers k such that a(k) = 0 see A138685.

			11=2+3^2 hence a(1)=3,
13=4+3^2 hence a(2)=3,
31=6+5^2 hence a(3)=5.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Near-Square Prime

Cf. A002373, A020481, A049613, A059324 (?).

a:= proc(n) local p;
      if irem(n, 3)=1 and not isprime(2*n+9) then 0
    else p:=2;
         do p:= nextprime(p);
            if isprime(2*n+p^2) then return p fi
         od
      fi
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 16 2014

a = {}; Do[ p = 0; While[ (! PrimeQ[ 2*n + Prime[ p + 1 ]2 ]) && (p < 1000), p++ ]; If[ p < 1000, AppendTo[ a, Prime[ p + 1 ] ], AppendTo[ a, 0 ] ], {n, 1, 150} ]; a (* Artur Jasinski, Mar 26 2008 *)
a[n_]:=If[Mod[n,3]!=1,(For[m=1,!PrimeQ[2n+Prime[m]^2],m++ ]; Prime[m]),If[ !PrimeQ[2n+9],0,3]];Table[a[n],{n,100}] (* Farideh Firoozbakht, Mar 28 2008 *)

More terms from Artur Jasinski and Farideh Firoozbakht, Mar 26 2008

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

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

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Magma

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A138479 a(n) = smallest prime p such that 2*n + p^2 is another prime, or 0 if no such prime exists.

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Maple

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

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Examples

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Maple

Mathematica

PARI

Formula

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

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Author

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Crossrefs

Programs

Mathematica

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

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

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