A270493 Integers n such that the n-th prime divides the n-th Pell number (A000129(n)).

3, 10, 45, 1710, 308961, 601929, 732202, 2214702, 7626372, 13976550, 21971144, 27575700, 207268867, 1014593260, 1134331652, 3140421935, 6196934304, 21338685403, 49990179304, 82456321500

Offset

1,1

Comments

For a(5), corresponding Pell number A000129(308961) has 118263 digits.

Any subsequent terms exceed 2*10^11. - Lucas A. Brown, Mar 08 2024

Links

Table of n, a(n) for n=1..20.

Lucas A. Brown, Python program.

Example

10 is a term because A000129(10) = 2378, A000040(10) = 29 and 2378 mod 29 = 0.

Mathematica

Select[Range[1, 10000], Divisible[Fibonacci[#, 2], Prime[#]] &] (* Vaclav Kotesovec, Mar 18 2016 *)

Prog

(PARI) a000129(n) = ([2, 1; 1, 0]^n)[2, 1];
for(n=1, 1e10, if(lift(Mod(a000129(n), prime(n))) == 0, print1(n, ", ")));
(Python) # See LINKS.

Crossrefs

Cf. A000040, A000129, A075702.

Sequence in context: A118601 A005143 A356572 * A121138 A355050 A371549

Adjacent sequences: A270490 A270491 A270492 * A270494 A270495 A270496

Keyword

nonn,more,hard

Author

Altug Alkan, Mar 18 2016

Extensions

a(6)-a(8) from Gheorghe Coserea, Mar 24 2016

a(9)-a(13) from Daniel Suteu, Nov 07 2019

a(14)-a(20) from Lucas A. Brown, Mar 08 2024

Status

approved