login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A006970 Euler pseudoprimes: 2^((n-1)/2) == +- 1 mod n.
(Formerly M5442)
11
341, 561, 1105, 1729, 1905, 2047, 2465, 3277, 4033, 4681, 5461, 6601, 8321, 8481, 10261, 10585, 12801, 15709, 15841, 16705, 18705, 25761, 29341, 30121, 31621, 33153, 34945, 41041, 42799 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Pseudoprimes for the primality test from [Schick]: n odd is probably prime if (n-1) | A003558((n-1)/2). (Succeeds for 99.9975% of odd natural numbers less than 10^8.) - Jonathan Skowera, Jun 29 2013

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, A12.

C. Schick, Weiche Primzahlen und das 257-Eck, 2008, pages 140-146.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Euler pseudoprimes up to 10^8; table of n, a(n) for n = 1..1231

Eric Weisstein's World of Mathematics, Euler Pseudoprime.

Index entries for sequences related to pseudoprimes

MATHEMATICA

ok[_?PrimeQ] = False; ok[n_] := (p = PowerMod[2, (n - 1)/2, n]; p == Mod[1, n] || p == Mod[-1, n]); Select[2 Range[22000] + 1, ok] (* Jean-Fran├žois Alcover, Apr 06 2011 *)

PROG

(PARI) isok(n) = {if (!isprime(n) && (n%2), npm = Mod(2, n)^((n-1)/2); if ((npm == Mod(1, n)) || (npm == Mod(-1, n)), print1(n, ", ")); ); } \\ Michel Marcus, Sep 12 2015

CROSSREFS

Sequence in context: A001567 A178723 A210993 * A007324 A007011 A064907

Adjacent sequences:  A006967 A006968 A006969 * A006971 A006972 A006973

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, Robert G. Wilson v, Richard Pinch

EXTENSIONS

a(15) corrected (to 10261 from 10241) by Faron Moller (fm(AT)csd.uu.se)

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 27 02:45 EDT 2017. Contains 284144 sequences.