A079953 Smallest prime p such that prime(n) mod 2*p = prime(n).

2, 2, 3, 5, 7, 7, 11, 11, 13, 17, 17, 19, 23, 23, 29, 29, 31, 31, 37, 37, 37, 41, 43, 47, 53, 53, 53, 59, 59, 59, 67, 67, 71, 71, 79, 79, 79, 83, 89, 89, 97, 97, 97, 97, 101, 101, 107, 113, 127, 127, 127, 127, 127, 127, 131, 137, 137, 137, 139, 149, 149, 149, 157, 157

Offset: 1

Author

Reinhard Zumkeller, Jan 19 2003

Keywords

• nonn
• easy

Comments

a(n) is smallest prime greater than prime(n)/2. - Peter Munn, Sep 18 2017

Examples

			n=6: prime(6)=13 and 13 mod(2*2)=1, 13 mod(2*3)=1, 13 mod(2*5)=3, 13 mod(2*7)=13, therefore a(6)=7.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A079952, A039734.

Programs

Mathematica

f[n_] := Block[{p = 2}, While[Prime@ n != Mod[Prime@ n, 2 p], p = NextPrime@ p]; p]; Array[f, 64] (* Michael De Vlieger, Mar 17 2015 *)

PARI

a(n,q=prime(n))=nextprime(q/2) \\ Charles R Greathouse IV, Mar 17 2015

Formula

T(n, A049084(a(n))) = A000040(n), T defined as in A079950.

a(n) = nextprime(prime(n)/2) ~ (n log n)/2. - Charles R Greathouse IV, Mar 17 2015

Conjecture: a(n) = A039734(n), n>=2. - R. J. Mathar, May 03 2021