A175682 Maximal run length of positive primes of the form ..., n-2*3*5, n-2*3, n-2, n, n+2, n+2*3, n+2*3*5, ...

0, 1, 2, 0, 4, 0, 2, 0, 0, 0, 4, 0, 3, 0, 0, 0, 5, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 9, 0, 4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, 4, 0, 0

Offset: 1

Author

Vladislav-Stepan Malakovsky and Juri-Stepan Gerasimov, Aug 08 2010

Keywords

• nonn

Examples

			For n=5, there is a run of primes from 5-A002110(1) to 5+A002110(2): [3, 5, 7, 11] (while 5-A002110(2) = 5-6 = -1 and 5+A002110(3) = 5+30 = 35 are not primes), thus a(5) = 4. - _Antti Karttunen_, Jan 03 2019
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A002110, A175663.

Programs

Mathematica

Array[If[PrimeQ@ #, Block[{s = {1}, t = {1}}, While[PrimeQ[# + Times @@ Prime@ s], AppendTo[s, s[[-1]] + 1]]; While[And[# > 0, PrimeQ[#]] &[# - Times @@ Prime@ t], AppendTo[t, t[[-1]] + 1]]; Last[s] + Last[t] - 1], 0] &, 105] (* Michael De Vlieger, Jan 03 2019 *)

PARI

A175682(n) = if(!isprime(n),0,my(pr=2, dn=1, dp=1, rl=1); for(k=1, oo, if(!isprime(n-pr), dn=0); if(!isprime(n+pr), dp=0); if(!(dn+dp), return(rl)); rl += (dn+dp); pr *= prime(1+k))); \\ (Note that isprime in PARI/GP 2.9.4 returns 0 on all negative arguments) - Antti Karttunen, Jan 03 2019

Formula

a(n) >= A175663(n). - Antti Karttunen, Jan 03 2019

Extensions

Terms a(5), a(7) and a(19) corrected by Antti Karttunen, Jan 03 2019