A348204 Fibonacci-like sequence of composite numbers with a(0) = 759135467284, a(1) = 74074527465.

759135467284, 74074527465, 833209994749, 907284522214, 1740494516963, 2647779039177, 4388273556140, 7036052595317, 11424326151457, 18460378746774, 29884704898231, 48345083645005, 78229788543236, 126574872188241, 204804660731477, 331379532919718, 536184193651195

Offset: 0

Author

Chittaranjan Pardeshi, Oct 06 2021

Keywords

• nonn
• easy

Comments

This is a second-order linear recurrence sequence with a(0) and a(1) coprime that does not contain any primes.

This sequence was found using Knuth's method.

Links

• R. L. Graham, A Fibonacci-Like sequence of composite numbers, Math. Mag., Vol. 37, No. 5 (1964), pp. 322-324.
• Donald E. Knuth, A Fibonacci-Like sequence of composite numbers, Math. Mag., Vol. 63, No. 1 (1990), pp. 21-25.
• Index entries for linear recurrences with constant coefficients, signature (1,1).

Crossrefs

Cf. A221286, A083104, A082411, A083105, A083216, A083216.

Programs

Maple

a:= n-> (<<0|1>, <1|1>>^n. <<759135467284, 74074527465>>)[1, 1]:
seq(a(n), n=0..16);  # Alois P. Heinz, Oct 06 2021

Mathematica

LinearRecurrence[{1, 1}, {759135467284, 74074527465}, 17] (* Amiram Eldar, Oct 07 2021 *)

PARI

a(n)=759135467284*fibonacci(n-1)+ 74074527465*fibonacci(n)

Formula

a(n) = a(n-1) + a(n-2).