A049653 -id:A049653 - cp's OEIS frontend

A060267 Difference between 2 closest primes surrounding 2n.

2, 2, 4, 4, 2, 4, 4, 2, 4, 4, 6, 6, 6, 2, 6, 6, 6, 4, 4, 2, 4, 4, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 4, 4, 2, 6, 6, 6, 4, 4, 6, 6, 6, 8, 8, 8, 8, 4, 4, 2, 4, 4, 2, 4, 4, 14, 14, 14, 14, 14, 14, 14, 4, 4, 6, 6, 6, 2, 10, 10, 10, 10, 10, 2, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 2, 10, 10, 10, 10, 10, 2, 4

Offset: 2

Labos Elemer, Mar 23 2001

nonn

			a(3) = 2 because the closest primes to 2*3 = 6 are (5,7) and the difference between these is 2. - _Michael De Vlieger_, Nov 02 2017

Michael De Vlieger, Table of n, a(n) for n = 2..10000

Cf. A020482, A049653, A060264, A060265, A060266, A060268.

with(numtheory): [seq(nextprime(2*i)-prevprime(2*i),i=2..256)];

Array[Subtract @@ NextPrime[#, {1, -1}] &[2 #] &, 96, 2] (* Michael De Vlieger, Nov 02 2017 *)
NextPrime[#]-NextPrime[#,-1]&/@(2*Range[2,100]) (* Harvey P. Dale, Nov 07 2017 *)

a(n) = nextprime(2*n+1) - precprime(2*n-1); \\ Michel Marcus, Sep 16 2020

A118747 a(n) = product[k=1..n] P(k), where P(k) is the largest prime <= 2*k. a(n) = product[k=1..n] A060308(k).

Original entry on oeis.org

2, 6, 30, 210, 1470, 16170, 210210, 2732730, 46456410, 882671790, 16770764010, 385727572230, 8871734161290, 204049885709670, 5917446685580430, 183440847252993330, 5686666264842793230, 176286654210126590130

Offset: 1

Jonathan Vos Post, Apr 29 2006

Cf. A020482, A049653, A060266-A060268, A060264, A060265, A060308, A118455, A118456, A118748.

A118752 a(n) = product[k=0..n] P(k), where P(k) is the smallest prime > 3*n. a(n) = product[k=0..n] A118751(k).

Original entry on oeis.org

2, 10, 70, 770, 10010, 170170, 3233230, 74364290, 2156564410, 62540367890, 1938751404590, 71733801969830, 2654150672883710, 108820177588232110, 4679267636293980730, 219925578905817094310, 11656055682008305998430

Offset: 0

Jonathan Vos Post, Apr 29 2006

Analogous to A118456 a(n) = product{k=1..n} P(k), where P(k) is the smallest prime >= k.

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. A020482, A049653, A060266-A060268, A060264, A060265, A060308, A118455, A118456, A118748-51.

Rest[FoldList[Times,1,Table[NextPrime[3n],{n,0,20}]]] (* Harvey P. Dale, Mar 09 2014 *)

Definition corrected by Harvey P. Dale, Mar 09 2014

A238737 a(n) = 2*n+2 - A224911(n).

Original entry on oeis.org

0, 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

Offset: 0

Paul Curtz, Mar 04 2014

nonn

It appears that a(n+2) is successively either one 1 or a string of the odd numbers.
Conjecture: the rank of 1's is A005097(n+1). This is another link between Bernoulli numbers and primes via A190339(n).
Apparently (essentially) a duplicate of A049653. - R. J. Mathar, Mar 30 2014

			a(0)=2-2=0, a(1)=4-3=1, a(2)=6-5=1, a(3)=8-7=1, a(4)=10-7=3.

Cf. A060308, A005408.

cp's OEIS Frontend

A060267 Difference between 2 closest primes surrounding 2n.

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A118747 a(n) = product[k=1..n] P(k), where P(k) is the largest prime <= 2*k. a(n) = product[k=1..n] A060308(k).

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A118752 a(n) = product[k=0..n] P(k), where P(k) is the smallest prime > 3*n. a(n) = product[k=0..n] A118751(k).

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A238737 a(n) = 2*n+2 - A224911(n).

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