NUMERO 144=12*12=SEXTO DIA (144 HORAS)=NUEVA JERUSALEN=12 DE LA SERIE FIBONACCI - FORO LIBREPENSADOR SIN CENSURA

Fibonacci 24 Repeating Pattern

The Fibonacci sequence has a pattern that repeats every 24 numbers.

Numeric reduction is a technique used in analysis of numbers in which all the digits of a number are added together until only one digit remains. As an example, the numeric reduction of 256 is 4 because 2+5+6=13 and 1+3=4.

Applying numeric reduction to the Fibonacci series produces an infinite series of 24 repeating digits:

1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9

If you take the first 12 digits and add them to the second twelve digits and apply numeric reduction to the result, you find that they all have a value of 9.

1st 12 numbers	1	1	2	3	5	8	4	3	7	1	8	9
2nd 12 numbers	8	8	7	6	4	1	5	6	2	8	1	9
Numeric reduction – Add rows 1 and 2	9	9	9	9	9	9	9	9	9	9	9	18
Final numeric reduction – Add digits of result	9	9	9	9	9	9	9	9	9	9	9	9

This pattern was contributed both by Joseph Turbeville and then again by a mathematician by the name of Jain.

We would expect a pattern to exist in the Fibonacci series since each number in the series encodes the sum of the previous two. What’s not quite so obvious is why this pattern should repeat every 24 numbers or why the first and last half of the series should all add to 9.

For those of you from the “Show Me” state, this pattern of 24 digits is demonstrated in the numeric reduction of the first 73 numbers of the Fibonacci series, as shown below:

Fibonacci Number	Numeric reduction by adding digits
Fibonacci Number	1st Level	2nd Level	Final Level
Example: 2,584	2+5+8+4=19	1+9=10	1+0=1
0	0	0	0
1	1	1	1
1	1	1	1
2	2	2	2
3	3	3	3
5	5	5	5
8	8	8	8
13	4	4	4
21	3	3	3
34	7	7	7
55	10	1	1
89	17	8	8
144	9	9	9
233	8	8	8
377	17	8	8
610	7	7	7
987	24	6	6
1,597	22	4	4
2,584	19	10	1
4,181	14	5	5
6,765	24	6	6
10,946	20	2	2
17,711	17	8	8
28,657	28	10	1
46,368	27	9	9
75,025	19	10	1
121,393	19	10	1
196,418	29	11	2
317,811	21	3	3
514,229	23	5	5
832,040	17	8	8
1,346,269	31	4	4
2,178,309	30	3	3
3,524,578	34	7	7
5,702,887	37	10	1
9,227,465	35	8	8
14,930,352	27	9	9
24,157,817	35	8	8
39,088,169	44	8	8
63,245,986	43	7	7
102,334,155	24	6	6
165,580,141	31	4	4
267,914,296	46	10	1
433,494,437	41	5	5
701,408,733	33	6	6
1,134,903,170	29	11	2
1,836,311,903	35	8	8
2,971,215,073	37	10	1
4,807,526,976	54	9	9
7,778,742,049	55	10	1
12,586,269,025	46	10	1
20,365,011,074	29	11	2
32,951,280,099	48	12	3
53,316,291,173	41	5	5
86,267,571,272	53	8	8
139,583,862,445	58	13	4
225,851,433,717	48	12	3
365,435,296,162	52	7	7
591,286,729,879	73	10	1
956,722,026,041	44	8	8
1,548,008,755,920	54	9	9
2,504,730,781,961	53	8	8
4,052,739,537,881	62	8	8
6,557,470,319,842	61	7	7
10,610,209,857,723	51	6	6
17,167,680,177,565	67	13	4
27,777,890,035,288	73	10	1
44,945,570,212,853	59	14	5
72,723,460,248,141	51	6	6
117,669,030,460,994	65	11	2
190,392,490,709,135	62	8	8
308,061,521,170,129	46	10	1
498,454,011,879,264	72	9	9

Thanks to Joseph Turbeville for sending “A Glimmer of Light from the Eye of a Giant” and to Helga Hertsig for bringing Jain’s discovery of this pattern to my attention.

Filed Under: Math

https://www.goldennumber.net/fibonacci-24-pattern/