Five Fives Game

[crispybits]

1001 = Σ5# + Σ5# + (Γ5 x Π5) - μ(5!!)
1001 = 465 + 465 + (24 x 3) - 1
1001 = 930 + 72 - 1
1001 = 1001

[maasman]

1002 = 5# x (5# + Π5) + 5!! - Π5
1002 = 30 x (30 + 3) + 15 - 3
1002 = 990 + 12
1002 = 1002

[crispybits]

1003 = 5# x (5# + Π5) + 5!! - σ(5!!)
1003 = 30 x (30 + 3) + 15 - 2
1003 = 990 + 13
1003 = 1003

You might not get me doing another one for a while maasman - I have stuff going on (nothing bad, just hectic) so will be turning these forums off for a little while. I will start up again once I have more time though.

[maasman]

Same for me essentially. Final stretch of school for this year and all.

1004 = 5# x (5# + Π5) + 5!! - μ(5!!)
1004 = 30 x (30 + 3) + 15 - 1
1004 = 990 + 14
1004 = 1004

[rishaed]

Insanity!!!! I smell insanity here! Where do you guys get the time to figure these out?????!!!

[maasman]

Insanity!!!! I smell insanity here! Where do you guys get the time to figure these out?????!!!

Most of it is just building off the previous. Pretty much all the basic numbers are figured out with these functions so it's really not too bad.

[crispybits]

OK lets see if this one can be bumped back into life....

1005 = ( σ(5!) - ( ( 5!! - σ(5!!) ) x Π5 ) ) x 5
1005 = ( 240 - ( ( 15 - 2 ) x 3 ) ) x 5
1005 = ( 240 - ( 13 x 3 ) ) x 5
1005 = ( 240 - 39 ) x 5
1005 = 201 x 5
1005 = 1005

(for anyone not in on this game for a while and confused by the greek double dutch-ness on that top line, there's a whole list of the silly symbols and what each can give you on page 20 right at the bottom inside a spoiler tag)

[maasman]

I was waiting for someone to come here again.

Here they are again:

Spoiler

n! = Factorial - n x (n-1) x (n-2) x …. x 3 x 2 x 1
n!! = Double Factorial - n x (n-2) x (n-4) x … x either (6 x 4 x 2) or (5 x 3 x 1)
Γn = Gamma function - (n-1)!
⌈n⌉ = Ceiling function - the smallest integer equal to or greater than n
⌊n⌋ = Floor function - the largest integer equal to or smaller than n
n# = Primorial - n! but only using the prime numbers
n$ = Superfactorial - n! x (n-1)! x (n-2)! x … x 3! x 2! x 1!
τ(n) = Ramanujan’s Tau function – can't explain this one but it exists and the list up to τ(28) is here: http://oeis.org/A000594/list
σ(n) = Divisor function – sum of all factors of n
Π(n) = Prime counting function – how many prime numbers exist up to and including n
μ(n) = Mobius function – if the number is a square it's 0, if the number is not a square and Π(n) is odd it's -1, and if it's not a square and Π(n) is even it's 1. List to μ(77) here: http://oeis.org/A008683/list (not incredibly useful except it gives us a single 5 way to get to 1 - μ(5!!) - so could come in handy now and then)
Σ(n) = Sum function – n + (n-1) + (n-2) + …… + 3 + 2 + 1
φ(n) = Euler’s totient function – number of numbers less than n which share no factors with n – list up to φ(69) here: http://oeis.org/A000010/list
σ(n) = the number of distinct primes that are factors of n. List up to σ(111) here: http://oeis.org/A001221/list (again not greatly useful except as a single 5 way to get to 2 - σ(5!!))

I'm going to cheat to start just to get my head back in it.

1006 = 5# x (5# + Π5) + 5!! + μ(5!!)
1006 = 30 x (30 + 3) + 15 + 1
1006 = 990 + 16
1006 = 1006

[crispybits]

1007 = (Γ5 - 5) x (55 - σ(5!!))
1007 = (24-5) x (55 - 2)
1007 = 19 x 53
1007 = 1007

[maasman]

1008 = 5# x (5# + Π5) + 5!! + Π5
1008 = 30 x (30 + 3) + 15 + 3
1008 = 990 + 18
1008 = 1008

[crispybits]

Bah I'm on the odds which means I will get all the awkward primes unless someone else joins in

1009 = (Σ(5#) x σ(5!!)) + (σ(Γ5) + σ(5#) + μ(5!!))
1009 = (465 x 2) + (36 + 42 + 1)
1009 = 930 + 79
1009 = 1009

[maasman]

1010 = 5# x (5# + Π5) + 5!! + 5
1010 = 30 x (30 + 3) + 15 + 5
1010 = 990 + 20
1010 = 1010

[crispybits]

1011 = (ΣΓ5 + 5# + 5 + σ(5!!)) x Π5
1011 = (300 + 30 + 5 + 2) x 3
1011 = 337 x 3
1011 = 1011

[maasman]

1012 = 5# x (5# + Π5) + Γ5 - σ(5!!)
1012 = 30 x (30 + 3) + 24 - 2
1012 = 990 + 22
1012 = 1012

[crispybits]

1013 = (Σ(5#) x σ(5!!)) + (σ(Γ5) + σ(5#) + 5)
1013 = (465 x 2) + (36 + 42 + 5)
1013 = 930 + 83
1013 = 1013

[maasman]

1014 = (σ(5!!)+σ(5!!))^5 - 5 - 5
1014 = (2 + 2)^5 - 10
1014 = 1024 - 10
1014 = 1014

[blackdragon1661]

I don't get it.

[Thorthoth]

1015 = 500 + 500 + 5 + 5 + 5
1015 = 1000 + 15
1015 = 1015