Music, History and the Mathematics of
Sequence Numbers:
A Tale of Two Famous Phone Numbers
“Beechwood 4-5789" is a song written
by Marvin Gaye, William "Mickey" Stevenson and George Gordy. It was a 1962 hit single for the Motown girl
group “The Marvelettes”. The title of
the song refers to a phone number – 234-5789.
If you want to listen to this song and see a picture of the Marvelettes
you can visit this YouTube website: https://www.youtube.com/watch?v=Us18AUBM2RI
We can create a “Beechwood 4-5789"
Heptanacci Sequence and it’s associated Sequence Number, based on this famous
phone number.
The “Beechwood 4-5789" Heptanacci
Sequence:
a(0) = a(1) = a(2) = a(3) = a(4) = a(5) =
0, a(6) = 1, and when n>6 then a(n) = 2*a(n-1) + 3*a(n-2) + 4*a(n-3) +
5*a(n-4) + 7*a(n-5) + 8*a(n-6) + 9*a(n-7).
The Sequence Number is:
9,999,999,999,997,999,999,999,999,699,999,999,999,959,999,
999,999,994,999,999,999,999,299,999,999,999,919,999,999, 999,991
1/99999999999979999999999996999999999999599999999
99994999999999999299999999999919999999999991 =
0.
0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000001 0000000000002 0000000000007 0000000000024 0000000000082 0000000000281 0000000000961 0000000003287 0000000011233 0000000038405 0000000131301 0000000448897 0000001534708 0000005246912 0000017938323 0000061328143 0000209670775 0000716829672 0002450721977 0008378612714 0028645089715 0097932819316 0334816095709 …
Terms are written in 13 digit strings so
that all terms up to 12 digits long will be accurate.
Terms are accurate up to the 23rd
non-zero term.
This sequence is not listed in the OEIS –
yet. Please compare these results with
the table below.
|
"The
Beachwood 4 - 5789"
|
"867-5309/Jenny"
|
|
Heptanaci
Sequence
|
Heptanacci
Sequence
|
|
a(0)
|
0
|
0
|
a(1)
|
0
|
0
|
a(2)
|
0
|
0
|
a(3)
|
0
|
0
|
a(4)
|
0
|
0
|
a(5)
|
0
|
0
|
a(6)
|
1
|
1
|
a(7)
|
2
|
8
|
a(8)
|
7
|
70
|
a(9)
|
24
|
615
|
a(10)
|
82
|
5,401
|
a(11)
|
281
|
47,431
|
a(12)
|
961
|
416,533
|
a(13)
|
3,287
|
3,657,951
|
a(14)
|
11,233
|
32,123,745
|
a(15)
|
38,405
|
282,107,385
|
a(16)
|
131,301
|
2,477,437,700
|
a(17)
|
448,897
|
21,756,600,088
|
a(18)
|
1,534,708
|
191,064,198,056
|
a(19)
|
5,246,912
|
|
a(20)
|
17,938,323
|
|
a(21)
|
61,328,143
|
|
a(22)
|
209,670,775
|
|
a(23)
|
716,829,672
|
|
a(24)
|
2,450,721,977
|
|
a(25)
|
8,378,612,714
|
|
a(26)
|
28,645,089,715
|
|
a(27)
|
97,932,819,316
|
|
a(28)
|
334,816,095,709
|
"867-5309/Jenny" is a song
written by Alex Call and Jim Keller and performed by Tommy Tutone that was
released on the album Tommy Tutone 2, on the Columbia Records label. It peaked
at #4 on the Billboard Hot 100 chart and #16 on the Billboard Top Tracks chart
in 1982. If you want to see a video of
Tommy Tutone singing this song you can visit the YouTube website: https://www.youtube.com/watch?v=6WTdTwcmxyo
This song actually started a nation wide
disturbance because of the number of people calling this number and asking for
Jenny. See the Wikipedia article: https://en.wikipedia.org/wiki/867-5309/Jenny
We can create a "867-5309/Jenny"
Heptanacci Sequence and it’s associated Sequence Number, based on this famous
phone number.
The "867-5309/Jenny" Heptanacci
Sequence:
a(0) = a(1) = a(2) = a(3) = a(4) = a(5) =
0, a(6) = 1, and when n>6 then a(n) = 8*a(n-1) + 6*a(n-2) + 7*a(n-3) +
5*a(n-4) + 3*a(n-5) + 0*a(n-6) + 9*a(n-7).
The Sequence Number is:
9,999,999,999,991,999,999,999,999,399,999,999,999,929,999,
999,999,994,999,999,999,999,699,999,999,999,999,999,999, 999,991
1/999999999999199999999999939999999999992999999
9999994999999999999699999999999999999999999991 =
0.
0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000000 0000000000001 0000000000008 0000000000070 0000000000615 0000000005401 0000000047431 0000000416533 0000003657951 0000032123745 0000282107385 0002477437700 0021756600088 0191064198056 …
Terms are written in 13 digit strings so
that all terms up to
12 digits long will be accurate.
Terms are accurate up to the 13th
non-zero term.
This sequence is not listed in the OEIS –
yet. Please compare
these results with the table above. |
Many people who were alive in the 1960 and
the 1980 can still remember these two phone numbers.
David
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