cp's OEIS Frontend

A099088 Indices of prime companion Pell numbers, divided by 2 (A001333).

%I A099088 #44 Feb 16 2025 08:32:54
%S A099088 2,3,4,5,7,8,16,19,29,47,59,163,257,421,937,947,1493,1901,6689,8087,
%T A099088 9679,28753,79043,129127,145969,165799,168677,170413,172243,278321,
%U A099088 552283
%N A099088 Indices of prime companion Pell numbers, divided by 2 (A001333).
%C A099088 Note that for A001333(n) to be prime, the index n must be prime or a power of 2. The indices greater than 421 yield probable primes.
%C A099088 Numbers n for which ((1+sqrt(2))^n + (1-sqrt(2))^n)/2 is prime. - _Artur Jasinski_, Dec 10 2006
%D A099088 F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, p. 62, 1983.
%H A099088 J. B. Cosgrave and K. Dilcher, <a href="https://fq.math.ca/Papers1/51-2/CosgraveDilcher-1.pdf">Pairs of reciprocal quadratic congruences involving primes</a>,  Fib. Quart. 51 (2) (2013) 98, after Theorem 3.
%H A099088 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PellNumber.html">Pell Number</a>
%H A099088 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes </a>
%t A099088 lst={}; a=1; b=1; Do[c=a+2b; a=b; b=c; If[PrimeQ[c], AppendTo[lst, n]], {n, 2, 10000}]; lst
%t A099088 (* Second program: *)
%t A099088 Do[If[PrimeQ[Expand[((1 + Sqrt[2])^n + (1 - Sqrt[2])^n)/2]], Print[n]], {n, 0, 1000}] (* _Artur Jasinski_, Dec 10 2006 *)
%o A099088 (PARI) isok(n) = isprime(polchebyshev(n, 1, I)/I^n); \\ _Michel Marcus_, Dec 07 2018
%Y A099088 Cf. A002203 (companion Pell numbers), A086395 (primes in A001333), A096650 (indices of prime Pell numbers).
%Y A099088 Cf. A005850.
%K A099088 hard,nonn
%O A099088 1,1
%A A099088 _T. D. Noe_, Sep 24 2004
%E A099088 a(24) from _Eric W. Weisstein_, May 22 2006
%E A099088 a(25) from _Eric W. Weisstein_, Aug 29 2006
%E A099088 a(26) from _Eric W. Weisstein_, Nov 11 2006
%E A099088 a(27) from _Eric W. Weisstein_, Nov 26 2006
%E A099088 a(28) from _Eric W. Weisstein_, Dec 10 2006
%E A099088 a(29) from _Eric W. Weisstein_, Jan 25 2007
%E A099088 a(30) from _Robert Price_, Dec 07 2018
%E A099088 a(31) from _Robert Price_, Dec 05 2023