A090097 -id:A090097

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A090096

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

+10
3

4, 1194649, 121, 1194649, 4, 4377277921, 25, 9, 4, 9, 5041, 7252249, 4, 841, 848615161, 1194649, 4, 25, 9, 78961, 4, 169, 169, 25, 4, 9, 121, 9, 4, 49, 49, 25, 4, 2129445719544546771481, 9, 4377277921, 4, 289, 64625521, 121, 4, 529, 25, 9, 4, 9

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..46.

Index entries for sequences related to pseudoprimes

FORMULA

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

EXAMPLE

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

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

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.

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

MATHEMATICA

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]}]

CROSSREFS

Cf. A007535, A090086, A247072, A039951.

KEYWORD

nonn,more

AUTHOR

Labos Elemer, Dec 01 2003

EXTENSIONS

More terms from Michel Marcus, Aug 30 2019

STATUS

approved

A090098

Bases such that the smallest prime-power-pseudoprime is belonging to equals 25.

+10
3

7, 18, 24, 32, 43, 51, 68, 74, 76, 99, 124, 126, 132, 151, 168, 174, 176, 182, 207, 218, 232, 243, 268, 274, 276, 282, 299, 318, 324, 326, 351, 374, 376, 382, 399, 407, 418, 426, 432, 443, 468, 474, 482, 499, 507, 518, 524, 526, 543, 551, 574, 576, 582, 599, 607

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Values of x such that A090096(x) = 25.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

MATHEMATICA

pspQ[n_, b_] := CompositeQ[n] && PowerMod[b, n - 1, n ] == 1 ; aQ[n_]:=pspQ[25, n] && AllTrue[{4, 8, 9, 16}, !pspQ[#, n] &]; Select[Range[1000], aQ] (* Amiram Eldar, Sep 09 2019 *)

CROSSREFS

Cf. A007535, A090086, A090096, A090097.