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Numbers that are Fibonacci numbers plus or minus 1.
3

%I #26 Jun 24 2023 07:55:09

%S 0,1,2,3,4,6,7,9,12,14,20,22,33,35,54,56,88,90,143,145,232,234,376,

%T 378,609,611,986,988,1596,1598,2583,2585,4180,4182,6764,6766,10945,

%U 10947,17710,17712,28656,28658,46367,46369,75024,75026,121392,121394,196417

%N Numbers that are Fibonacci numbers plus or minus 1.

%C Only the first four terms are Fibonacci numbers per se. - _Alonso del Arte_, Oct 05 2017

%H Harry J. Smith, <a href="/A061489/b061489.txt">Table of n, a(n) for n=1..500</a>

%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibmaths.html">The Mathematical Magic of the Fibonacci Numbers</a>.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-1,1,1,1,1).

%F a(n) = -a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n+5), for n >= 10. - _Amiram Eldar_, Jun 24 2023

%t Union[Table[Fibonacci[i] - 1, {i, 30}], Table[Fibonacci[j] + 1, {j, 0, 30}]]

%t Union[Flatten[# + {1, -1} &/@ Fibonacci[Range[30]]]] (* _Harvey P. Dale_, Dec 26 2015 *)

%o (PARI) { t="b061489.txt"; for (n=1, 4, write(t, n, " ", n - 1) ); g=3; h=2; for (n=3, 250, f=g + h; h=g; g=f; write(t, 2*n - 1, " ", f - 1); write(t, 2*n, " ", f + 1) ) } \\ _Harry J. Smith_, Jul 23 2009

%Y Cf. A000071, A001611 (the union of those two sequences forms this sequence).

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, Nov 08 2001

%E More terms from _Robert G. Wilson v_, Nov 12 2001