A175682 - OEIS

%I #17 Aug 22 2021 13:33:00

%S 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,

%T 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,

%U 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

%N 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, ...

%H Antti Karttunen, <a href="/A175682/b175682.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A175682/a175682.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

%F a(n) >= A175663(n). - _Antti Karttunen_, Jan 03 2019

%e 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

%t 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 *)

%o (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

%Y Cf. A002110, A175663.

%K nonn

%O 1,3

%A Vladislav-Stepan Malakovsky and _Juri-Stepan Gerasimov_, Aug 08 2010

%E Terms a(5), a(7) and a(19) corrected by _Antti Karttunen_, Jan 03 2019