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A047713 Euler-Jacobi pseudoprimes: 2^{(n-1)/2} == (2 / n) mod n, where (2 / n) is a Jacobi symbol.
(Formerly M5461)
5
561, 1105, 1729, 1905, 2047, 2465, 3277, 4033, 4681, 6601, 8321, 8481, 10585, 12801, 15841, 16705, 18705, 25761, 29341, 30121, 33153, 34945, 41041, 42799, 46657, 49141, 52633, 62745, 65281, 74665, 75361, 80581, 85489, 87249, 88357, 90751, 104653 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Odd composite numbers n such that 2^((n-1)/2) == (-1)^((n^2-1)/8) mod n. - Thomas Ordowski, Dec 21 2013

REFERENCES

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

H. Riesel, Prime numbers and computer methods for factorization, Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985.

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

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Euler-Jacobi Pseudoprime.

Eric Weisstein's World of Mathematics, Pseudoprime.

Index entries for sequences related to pseudoprimes

MATHEMATICA

Select[ Range[ 3, 105000, 2 ], Mod[ 2^((# - 1)/2) - JacobiSymbol[ 2, # ], # ] == 0 && ! PrimeQ[ # ] & ]

PROG

(PARI) is(n)=n%2 && Mod(2, n)^(n\2)==kronecker(2, n) && !isprime(n) \\ Charles R Greathouse IV, Dec 20 2013

CROSSREFS

Cf. A002997, A001567, A048950.

Sequence in context: A135721 A290486 A253595 * A006971 A270698 A218483

Adjacent sequences:  A047710 A047711 A047712 * A047714 A047715 A047716

KEYWORD

nonn,nice

AUTHOR

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

EXTENSIONS

Corrected by Eric W. Weisstein; more terms from David W. Wilson

STATUS

approved

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Last modified August 18 17:55 EDT 2018. Contains 313834 sequences. (Running on oeis4.)