A090125 a(n) is the least positive integer such that nextprime(a(n)^n) - prevprime(a(n)^n) = 4.

5, 3, 2, 2, 411, 195, 2, 392, 141, 105, 1161, 909, 69, 3243, 171, 370, 1659, 165, 26289, 1065, 8541, 19593, 43521, 1323, 84651, 25767, 25641, 7029, 63009, 693, 231, 957, 2601, 7137, 368265, 14769, 8169, 13071, 23679, 45, 13875, 6693, 136611, 34869, 55725, 4887, 231, 1935, 730071, 10305

Offset: 1

Author

Labos Elemer, Jan 12 2004

Keywords

• nonn

Examples

			with q-p=4,q,p are primes:
n=1:a(1)=5 because {p=3,a(1)^1=5,q=5};
n=7:a(7)=2 because {p=127,a(7)^7=128, q=131};
n=10:a(10)=105 because {p=c-2,c=a(10)^10=162889462677744140625,q=c+2}
		

Links

• Daniel Suteu, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A090121, A090122, A090123, A090124.

Programs

Mathematica

Table[fla=1;Do[If[((PrimeQ[s=n^k-3]&&PrimeQ[s1=n^k+1]) ||(PrimeQ[s=n^k-2]&&PrimeQ[s1=n^k+2])||(PrimeQ[s=n^k-1] &&PrimeQ[s1=n^k+3]))&&Equal[fla, 1]&&!Equal[n, 1], Print[{n, p, n^k, q, {k}}];fla=0], {n, 1, 1000000}], {k, 1, 60}]

PARI

a(n) = {my(k=1); while (nextprime(k^n+1) - precprime(k^n-1) != 4, k++); k;} \\ Michel Marcus, Sep 03 2019

PARI

f(k,r) = ispseudoprime(k-r) && ispseudoprime(k-r+4);
a(n) = for(k=1, oo, my(t=k^n); if((f(t,1) || f(t,2) || f(t,3)) && nextprime(t+1)-precprime(t-1)==4, return(k))); \\ Daniel Suteu, Sep 03 2019

Extensions

a(2) corrected and a(45)-a(50) from Daniel Suteu, Sep 03 2019