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

Author

Amiram Eldar, Nov 08 2019

Keywords

• nonn

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.

Crossrefs

Cf. A001567, A005845.

Programs

Mathematica

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