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A272627
Numbers n = pq where p, q are primes congruent to 3 and 7 mod 8, respectively.
1
21, 69, 77, 93, 133, 141, 213, 237, 253, 301, 309, 341, 381, 413, 437, 453, 469, 501, 517, 573, 581, 589, 597, 669, 717, 749, 781, 789, 813, 869, 893, 917, 933, 973, 989, 1077, 1101, 1133, 1141, 1149, 1253, 1293, 1317, 1333, 1349, 1357, 1389, 1397, 1437, 1461
OFFSET
1,1
COMMENTS
Candidate moduli for Rabin cryptosystem using Williams padding to ensure sufficient redundancy that the decryption is unique.
REFERENCES
Steven D. Galbraith, Mathematics of Public Key Cryptography, Cambridge University Press, 2012, page 493.
LINKS
H. C. Williams, A Modification of the RSA public encryption procedure, IEEE Trans. Inf. Theory 26(6) (1980), 726-729.
MATHEMATICA
With[{upto = 1000},
With[{primes = Prime@Range@PrimePi@NextPrime[upto/3]},
With[{p = Pick[primes, Mod[primes, 8], 3], q = Pick[primes, Mod[primes, 8], 7]},
Select[Union[Flatten@Outer[Times, p, q]], # <= upto &]] ]] (* after Harvey P. Dale at A016105 *)
PROG
(PARI) ok(n)={n%8==5 && bigomega(n)==2 && factor(n)[1, 1] % 4 == 3} \\ Andrew Howroyd, Dec 23 2019
CROSSREFS
Cf. A016105.
Sequence in context: A180758 A197121 A175461 * A043339 A023712 A045124
KEYWORD
nonn
AUTHOR
Morgan L. Owens, May 03 2016
EXTENSIONS
Terms a(36) and beyond from Andrew Howroyd, Dec 23 2019
STATUS
approved