A329240 - OEIS

%I #11 Dec 14 2019 21:21:54

%S 2465,219781,228241,252601,399001,512461,722261,741751,852841,1024651,

%T 1193221,1533601,1690501,1735841,1857241,1909001,2100901,2165801,

%U 2531845,2603381,2704801,2757241,3568661,3828001,4504501,5049001,5148001,5481451,6189121,6368689,6840001

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

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

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

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

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

%H Amiram Eldar, <a href="/A329240/b329240.txt">Table of n, a(n) for n = 1..655</a> (terms below 10^10)

%H H. J. A. Duparc, Belevenissen met van der Poel, in <a href="https://repository.tudelft.nl/islandora/object/uuid%3A134ee873-4d89-4ae2-873c-0f36d028ecb3">Vooruitgang bit voor bit: Liber Amicorum ac Collegarum bij het afscheid van Prof. dr. ir. W.L. van der Poel, 26 oktober 1988</a>, Delftse Universitaire Pers, 1988.

%H Erik Lieuwens, <a href="https://repository.tudelft.nl/islandora/object/uuid:becf731b-0b3c-4b2f-8479-9d4f205659d9?collection=research">Fermat pseudo primes</a>, Doctoral Thesis, Delft University of Technology, 1971, pp. 29-30.

%H Willem Louis van der Poel, Primality tests with higher order recurrent sequences, in <a href="https://repository.tudelft.nl/islandora/object/uuid%3A7fb929f3-f651-40ec-bb55-05d888cfd76b">Recursie in retrospectief; voordrachten ter gelegenheid van het veertigjarig doctorsjubileum van Prof. dr. H.J.A. Duparc</a>, Delft University of Technology, 1994.

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

%Y Cf. A001567, A005845.

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 08 2019