A071683 Nonprimes which are the average of two consecutive Fibonacci numbers.

1, 4, 72, 305, 1292, 5473, 23184, 98209, 416020, 1762289, 7465176, 31622993, 133957148, 567451585, 2403763488, 10182505537, 43133785636, 182717648081, 774004377960, 3278735159921, 13888945017644, 58834515230497

Offset

1,2

Comments

Prove that 17 is the only prime which is the average of two consecutive Fibonacci numbers.

This is not such a proof, but 17 is the only prime which is the average of two consecutive Fibonacci numbers for the first 40,000 such numbers. - Harvey P. Dale, Mar 23 2025

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

f[n_] := Fibonacci[n]; a = Select[ Range[70], IntegerQ[(f[ # ] + f[ # + 1])/2] && !PrimeQ[(f[ # ] + f[ # + 1])/2] &]; (f[a] + f[a + 1])/2
Select[Mean/@Partition[Fibonacci[Range[100]], 2, 1], IntegerQ[#]&&!PrimeQ[#]&] (* Harvey P. Dale, Mar 23 2025 *)

Crossrefs

Cf. A018252, A000045.

Sequence in context: A203537 A095385 A375251 * A386560 A192826 A190398

Adjacent sequences: A071680 A071681 A071682 * A071684 A071685 A071686

Keyword

nonn

Author

G. L. Honaker, Jr., Jun 22 2002

Extensions

Edited by Robert G. Wilson v, Jun 27 2002

Status

approved