A329240 Numbers that are both Fermat pseudoprimes to base 2 (A001567) and Bruckman-Lucas pseudoprimes (A005845).

2465, 219781, 228241, 252601, 399001, 512461, 722261, 741751, 852841, 1024651, 1193221, 1533601, 1690501, 1735841, 1857241, 1909001, 2100901, 2165801, 2531845, 2603381, 2704801, 2757241, 3568661, 3828001, 4504501, 5049001, 5148001, 5481451, 6189121, 6368689, 6840001

Offset

1,1

Comments

Van der Poel calculated the 215 terms below 6*10^8.

Van Zijl published the terms between 10^7 and 10^8.

These numbers were named "Van der Poel numbers" by Herman J. A. Duparc (1918-2002).

References

R. F. van Zijl, De getallen van Van der Poel (in Dutch), Master's thesis, Afstudeerverslag TU Delft, 1968.

Links

Amiram Eldar, Table of n, a(n) for n = 1..655 (terms below 10^10)

H. J. A. Duparc, Belevenissen met van der Poel, in Vooruitgang bit voor bit: Liber Amicorum ac Collegarum bij het afscheid van Prof. dr. ir. W.L. van der Poel, 26 oktober 1988, Delftse Universitaire Pers, 1988.

Erik Lieuwens, Fermat pseudo primes, Doctoral Thesis, Delft University of Technology, 1971, pp. 29-30.

Willem Louis van der Poel, Primality tests with higher order recurrent sequences, in Recursie in retrospectief; voordrachten ter gelegenheid van het veertigjarig doctorsjubileum van Prof. dr. H.J.A. Duparc, Delft University of Technology, 1994.

Mathematica

Select[Range[10^6], CompositeQ[#] && PowerMod[2, # - 1, #] == 1 && Divisible[LucasL[#] - 1, #] &]

Crossrefs

Cf. A001567, A005845.

Sequence in context: A304554 A152497 A365022 * A182381 A284089 A252113

Adjacent sequences: A329237 A329238 A329239 * A329241 A329242 A329243

Keyword

nonn

Author

Amiram Eldar, Nov 08 2019

Status

approved