A161503 a(n) = NextPrime(n^n) - PrevPrime(n^n).

2, 6, 6, 16, 14, 6, 46, 20, 52, 104, 54, 28, 44, 80, 72, 92, 172, 20, 142, 34, 110, 134, 130, 98, 106, 78, 174, 306, 26, 132, 54, 258, 116, 78, 50, 90, 448, 66, 214, 302, 140, 352, 466, 246, 670, 594, 396, 20, 244, 228, 640, 546, 462, 354, 1040, 408, 176, 564, 760

Offset: 2

Author

Vladimir Joseph Stephan Orlovsky, Jun 11 2009

Keywords

• nonn

Examples

			3 <- 2^2 -> 5; 5 - 3 = 2;
23 <- 3^3 -> 29; 29 - 23 = 6.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A074966, A074967.

Cf. A000312, A013633.

Programs

Maple

for n from 2 to 100 do nn := n^n ; printf("%d,",nextprime(nn)-prevprime(nn) ) ; od: # R. J. Mathar, Jun 12 2009

Mathematica

PrimeNext[n_]:=Module[{k},k=n+1;While[ !PrimeQ[k],k++ ];k]; PrimePrev[n_]:=Module[{k}, k=n-1;While[ !PrimeQ[k],k-- ];k]; DeltaY[n_]:=PrimeNext[n]-PrimePrev[n]; lst={};Do[AppendTo[lst,DeltaY[n^n]],{n,2,5!}];lst
npnn[n_]:=Module[{nn=n^n},NextPrime[nn]-NextPrime[nn,-1]]; Array[npnn,60,2] (* Harvey P. Dale, Dec 07 2013 *)

Formula

a(n) = A074966(n) + A074967(n) = A013633(A000312(n)). - R. J. Mathar, Jun 12 2009

Extensions

Offset changed by R. J. Mathar, Jun 12 2009