A338011 -id:A338011 - cp's OEIS frontend

A338007 Odd composite integers m such that A001906(m)^2 == 1 (mod m).

9, 21, 63, 99, 231, 323, 329, 369, 377, 423, 451, 861, 903, 1081, 1189, 1443, 1551, 1819, 1833, 1869, 1891, 2033, 2211, 2737, 2849, 2871, 2961, 3059, 3289, 3653, 3689, 3827, 4059, 4089, 4179, 4181, 4879, 5671, 5777, 6447, 6479, 6601, 6721, 6903, 7743

Offset: 1

Ovidiu Bagdasar, Oct 06 2020

nonn

For a, b integers, the generalized Lucas sequence is defined by the relation  U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1.
This sequence satisfies the relation U(p)^2 == 1 for p prime and b=1,-1.
The composite numbers with this property may be called weak generalized Lucas pseudoprimes of parameters a and b.
The current sequence is defined for a=3 and b=1.

D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020).

Dorin Andrica and Ovidiu Bagdasar, On Generalized Lucas Pseudoprimality of Level k, Mathematics (2021) Vol. 9, 838.
D. Andrica and O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, preprint for Mediterr. J. Math. 18, 47 (2021).

Cf. A338008 (a=4, b=1), A338009 (a=5, b=1), A338010 (a=6, b=1), A338011 (a=7, b=1).

Select[Range[3, 8000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 3/2]*ChebyshevU[#-1, 3/2] - 1, #] &]

A338008 Odd composite integers m such that A001353(m)^2 == 1 (mod m).

Original entry on oeis.org

35, 65, 91, 209, 455, 533, 595, 629, 679, 901, 923, 989, 1001, 1241, 1295, 1495, 1547, 1729, 1769, 1855, 1961, 1991, 2015, 2345, 2431, 2509, 2555, 2639, 2701, 2795, 2911, 3007, 3059, 3367, 3439, 3535, 3869, 3977, 4277, 4823, 5249, 5291, 5551, 5719, 5777

Offset: 1

Ovidiu Bagdasar, Oct 06 2020

nonn

For a, b integers, the generalized Lucas sequence is defined by the relation  U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1.
This sequence satisfies the relation U(p)^2 == 1 for p prime and b=1,-1.
The composite numbers with this property may be called weak generalized Lucas pseudoprimes of parameters a and b.
The current sequence is defined for a=4 and b=1.

D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020).

D. Andrica and O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, preprint for Mediterr. J. Math. 18, 47 (2021).

Cf. A338007 (a=3, b=1), A338009 (a=5, b=1), A338010 (a=6, b=1), A338011 (a=7, b=1).

Select[Range[3, 6000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 2]*ChebyshevU[#-1, 2] - 1, #] &]

A338009 Odd composite integers m such that A004254(m)^2 == 1 (mod m).

Original entry on oeis.org

25, 55, 115, 209, 253, 275, 319, 391, 425, 527, 551, 575, 713, 715, 775, 779, 935, 1105, 1111, 1265, 1705, 1807, 1919, 2015, 2035, 2071, 2575, 2627, 2893, 2915, 2929, 3281, 3289, 3655, 4031, 4033, 4141, 4199, 4355, 5191, 5291, 5671, 5699, 5777, 5885, 5983

Offset: 1

Ovidiu Bagdasar, Oct 06 2020

nonn

For a, b integers, the generalized Lucas sequence is defined by the relation U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1.
This sequence satisfies the relation U(p)^2 == 1 for p prime and b=1,-1.
The composite numbers with this property may be called weak generalized Lucas pseudoprimes of parameters a and b.
The current sequence is defined for a=5 and b=1.

D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020).

Dorin Andrica and Ovidiu Bagdasar, On Generalized Lucas Pseudoprimality of Level k, Mathematics (2021) Vol. 9, 838.
D. Andrica and O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, preprint for Mediterr. J. Math. 18, 47 (2021).

Cf. A338007 (a=3, b=1), A338008 (a=4, b=1), A338010 (a=6, b=1), A338011 (a=7, b=1).

Select[Range[3, 5985, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 5/2]*ChebyshevU[#-1, 5/2] - 1, #] &]

A338010 Odd composite integers m such that A001109(m)^2 == 1 (mod m).

Original entry on oeis.org

9, 35, 51, 55, 77, 85, 119, 153, 169, 171, 187, 209, 261, 319, 369, 385, 451, 531, 551, 595, 649, 715, 741, 779, 899, 935, 961, 969, 989, 1105, 1121, 1189, 1241, 1309, 1443, 1469, 1479, 1711, 1829, 1989, 2001, 2047, 2091, 2261, 2345, 2419, 2555, 2849, 2915

Offset: 1

Ovidiu Bagdasar, Oct 06 2020

nonn

For a, b integers, the generalized Lucas sequence is defined by the relation  U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1.
This sequence satisfies the relation U(p)^2 == 1 for p prime and b=1,-1.
The composite numbers with this property may be called weak generalized Lucas pseudoprimes of parameters a and b.
The current sequence is defined for a=6 and b=1.

D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020).

D. Andrica and O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, preprint for Mediterr. J. Math. 18, 47 (2021).

Cf. A338007 (a=3, b=1), A338008 (a=4, b=1), A338009 (a=5, b=1), A338011 (a=7, b=1).

Select[Range[3, 3000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 3]*ChebyshevU[#-1, 3] - 1, #] &]

cp's OEIS Frontend

A338007 Odd composite integers m such that A001906(m)^2 == 1 (mod m).

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A338008 Odd composite integers m such that A001353(m)^2 == 1 (mod m).

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A338009 Odd composite integers m such that A004254(m)^2 == 1 (mod m).

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Mathematica

A338010 Odd composite integers m such that A001109(m)^2 == 1 (mod m).

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica