A090096 - OEIS

%I #34 Aug 30 2019 16:55:11

%S 4,1194649,121,1194649,4,4377277921,25,9,4,9,5041,7252249,4,841,

%T 848615161,1194649,4,25,9,78961,4,169,169,25,4,9,121,9,4,49,49,25,4,

%U 2129445719544546771481,9,4377277921,4,289,64625521,121,4,529,25,9,4,9

%N Least n-pseudoprime which is a power of a prime number; smallest prime-power pseudoprime to base n.

%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>

%F a(n) = A039951(n)^2.

%e n=2: -1+2^(1092*1094) = K*1093*1093 = K*1194649;

%e n=4k+1: a(4k+1)=4; for a(k)=9 see A090097; a(k)=25 see A090098.

%e Some large values after a(46): a(52)=219521; a(56)=418609; a(58)=17161; a(59)=7711729; a(83)=23726641; a(84)=26569; a(86)=4656561121; a(87)=3996001; a(92)=528529; a(95)=4566769; a(96)=11881.

%e Hard bases below 100 are 47, 66, 72, 88, 90.

%t t=list-of-true-p-powers-generated-independently lf[x_] := Length[FactorInteger[x]] base=6;Do[s=Mod[ -1+base^(Part[t, n]-1), Part[t, n]]; If[Equal[s, 0], Print[Part[t, n]]], {n, 1, Length[t]}]

%Y Cf. A007535, A090086, A247072, A039951.

%K nonn,more

%O 1,1

%A _Labos Elemer_, Dec 01 2003

%E More terms from _Michel Marcus_, Aug 30 2019