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

%I A181781 #34 Feb 16 2025 08:33:13
%S A181781 21,25,33,45,49,57,65,69,77,85,91,93,105,117,121,125,129,133,141,145,
%T A181781 153,161,165,169,175,177,185,189,201,205,209,213,217,221,225,231,237,
%U A181781 245,247,249,253,259,261,265,273,285,289,297,301,305,309,321,325,329,333,341,343,345
%N A181781 Numbers n that are Euler pseudoprimes to some base b, 2 <= b <= n-2.
%H A181781 Amiram Eldar, <a href="/A181781/b181781.txt">Table of n, a(n) for n = 1..10000</a>
%H A181781 Karsten Meyer, <a href="http://de.wikibooks.org/wiki/Pseudoprimzahlen:_Tabelle_Pseudoprimzahlen_%2815_-_4999%29">Tabelle Pseudoprimzahlen (15-4999)</a>
%H A181781 Karsten Meyer, <a href="/A181781/a181781.txt">Rexx program</a>
%H A181781 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/EulerPseudoprime.html">MathWorld: Euler Pseudoprime</a>
%p A181781 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:
%p A181781 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:
%p A181781 for n from 3 to 800 do if isA181781(n) then printf("%d,",n) ; end if; end do: # _R. J. Mathar_, May 30 2011
%t A181781 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 *)
%o A181781 (See Rexx program in Links.)
%Y A181781 Cf. A006970, A181780.
%K A181781 nonn
%O A181781 1,1
%A A181781 _Karsten Meyer_, Nov 12 2010
%E A181781 Definition corrected by _Max Alekseyev_, Nov 12 2010
%E A181781 Edited definition to be consistent with OEIS style. - _N. J. A. Sloane_, Nov 13 2010