A181781 Numbers n that are Euler pseudoprimes to some base b, 2 <= b <= n-2.

21, 25, 33, 45, 49, 57, 65, 69, 77, 85, 91, 93, 105, 117, 121, 125, 129, 133, 141, 145, 153, 161, 165, 169, 175, 177, 185, 189, 201, 205, 209, 213, 217, 221, 225, 231, 237, 245, 247, 249, 253, 259, 261, 265, 273, 285, 289, 297, 301, 305, 309, 321, 325, 329, 333, 341, 343, 345

Offset: 1

Author

Karsten Meyer, Nov 12 2010

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Karsten Meyer, Tabelle Pseudoprimzahlen (15-4999)
• Karsten Meyer, Rexx program
• Eric W. Weisstein, MathWorld: Euler Pseudoprime

Crossrefs

Cf. A006970, A181780.

Programs

Maple

isEulPSP := proc(n,b) if isprime(n) then false; else m := modp(b &^ ((n-1)/2),n) ; if m= 1 or m = n-1 then true; else false; end if; end if;end proc:
isA181781 := proc(n) for b from 2 to n-2 do if isEulPSP(n,b) then return true; end if; end do: return false;end proc:
for n from 3 to 800 do if isA181781(n) then printf("%d,",n) ; end if; end do: # R. J. Mathar, May 30 2011

Mathematica

fQ[n_?PrimeQ, b_] = False; fQ[n_, b_] := Block[{p = PowerMod[b, (n - 1)/2, n]}, p == Mod[1, n] || p == Mod[-1, n]]; gQ[n_] := AnyTrue[Range[2, n - 2], fQ[n, #] &]; Select[2 Range[172] + 1, gQ] (* Michael De Vlieger, Sep 09 2015, after Jean-François Alcover at A006970, Version 10 *)

Extensions

Definition corrected by Max Alekseyev, Nov 12 2010

Edited definition to be consistent with OEIS style. - N. J. A. Sloane, Nov 13 2010