A207820 Let A = A025584. a(n) is the smallest A(m) such that the interval (A(m)*n, A(m+1)*n) contains no primes from A.

2, 2, 2, 1783, 967, 1663, 3187, 4813, 13873, 20347, 1783, 2617, 27743, 14533, 54829, 71143, 66169, 46687, 44119, 57787, 79609, 552883, 21397, 297079, 1187107, 89017, 798697, 285763, 761377, 2660587, 812047, 1463257, 2795059, 2816239, 2676727, 3069607, 2500297

Offset: 1

Author

Vladimir Shevelev and Peter J. C. Moses, Jan 10 2013

Keywords

• nonn

Comments

Conjecture. For n>=3, every a(n) is the lesser of a pair of cousin primes p and p+4, cf. A023200.

The limit of a(n) as n goes to infinity is infinity.

Crossrefs

Cf. A025584, A023200, A195325.

Programs

Mathematica

Table[aPrime[[NestWhile[#1+1&,1,!(nextAPrime[n aPrime[[#1]]]>n aPrime[[#1+1]])&]]],{n,2,20}]

PARI

is_a025584(x) = isprime(x) && !isprime(x-2)
a025584_next(n) = {local(p); p=n+1; while(!is_a025584(p), p=p+1); p}
no_a025584(a,b) = {local(x,r); r=1; for(x=a+1, b-1, if(is_a025584(x), r=0)); r}
a207820(n) = {local(r,rp); rp=2; r=3; while(!no_a025584(n*rp, n*r), rp=r; r=a025584_next(r)); rp} \\ Michael B. Porter, Jan 20 2013

Extensions

a(21)-a(37) from Michael B. Porter, Jan 20 2013