Sierpinski Number of the First Kind

Author

Eric W. Weisstein
November 16, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/SierpinskiNumbersoftheFirstKind.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/SierpinskiNumbersoftheFirstKind.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Numbers

SierpinskiS[n_]:=n^n+1
SierpinskiSk[k_]:=SierpinskiS[2^2^k]

SierpinskiS/@Range[10]

Prime

Table[k+2^k,{k,0,10}]

Most[s=SierpinskiSk/@Range[0,4]]

SierpinskiSk[5];//Timing

PrimeQ[s]

FactorInteger[SierpinskiSk[2]]//Timing

IntegerQ[SierpinskiSk[3]/(39 2^13+1)]

FactorInteger[SierpinskiSk[3]]//Timing

SierpinskiSk[11]/(591909  2^2063+1)

Digits

Length/@IntegerDigits/@s

Ceiling[Table[2^(k+2^k) Log[2]/Log[10],{k,0,5}]]

First Unknown Case

N[Log[10,Log[10,2]]+(k+2^k)Log[2]/.k->70]