9/29/2015
Music, History and the Mathematics of
Sequence Numbers:
A Tale of Two Famous Phone Numbers
“Beechwood 45789" 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 – 2345789.
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 45789"
Heptanacci Sequence and it’s associated Sequence Number, based on this famous
phone number.
The “Beechwood 45789" 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(n1) + 3*a(n2) + 4*a(n3) +
5*a(n4) + 7*a(n5) + 8*a(n6) + 9*a(n7).
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 23^{rd}
nonzero term.
This sequence is not listed in the OEIS –
yet. Please compare these results with
the table below.


"The
Beachwood 4  5789"

"8675309/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


"8675309/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
We can create a "8675309/Jenny"
Heptanacci Sequence and it’s associated Sequence Number, based on this famous
phone number.
The "8675309/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(n1) + 6*a(n2) + 7*a(n3) +
5*a(n4) + 3*a(n5) + 0*a(n6) + 9*a(n7).
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 13^{th}
nonzero 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