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A270493
Integers n such that the n-th prime divides the n-th Pell number (A000129(n)).
1
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
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
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