Repunit
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler in his book Recreations in the Theory of Numbers.
A repunit prime is a repunit that is also a prime number. Primes that are repunits in base 2 are Mersenne primes.
Definition
The base-b repunits are defined as (this b can be either positive or negative)
Thus, the number Rn(b) consists of n copies of the digit 1 in base b representation. The first two repunits base b for n=1 and n=2 are
In particular, the decimal (base-10) repunits that are often referred to as simply repunits are defined as
Thus, the number Rn = Rn(10) consists of n copies of the digit 1 in base 10 representation. The sequence of repunits base 10 starts with
Similarly, the repunits base 2 are defined as
Thus, the number Rn(2) consists of n copies of the digit 1 in base 2 representation. In fact, the base-2 repunits are the well-known Mersenne numbers Mn = 2n − 1, they start with
Podcasts:
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by Rah Band
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by Rah Band
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by Rah Band
Clouds Across The Moon
by: Rah BandINTRO
"Good evening. This is the intergalactic operator. Can I help you?"
"Yes. I'm trying to reach flight commander P.R. Johnson, on Mars, flight 2-4-7"
"Very well, hold on please [beeping] you're through!"
"Thank you operator!"
VERSE 1 :
Hi darlin' ! How are you doing ?
Hey baby, where're your sleeping ?
Oh I'm sorry, but I've been really missing you !
Hi darlin' ! How's the weather?
Say baby, is that cold better now ?
Oh I'm sorry, is there someone there with you??
BRIDGE:
Ooooh...since you went away, there's nothing goin' right !
I just can't sleep alone at night... I'm not ashamed to say
I badly need a friend...or it's the end.
CHORUS:
Now, when I look at the cloud's across the moon.
Here in the night I just hope and pray that soon.
Oh baby, you'll hurry home to me.
VERSE 2 :
Hi darlin', the kids say they love you.
Hey baby, is everything fine with you?
Please forgive me, but I'm trying not to cry...
BRIDGE :
Ooooh...I've had a million different lovers on the phone.
But I just stayed right here at home.
I don't think that I can take it anymore this crazy war.
CHORUS
"I'm sorry to interrupt your conversation, but we are
experiencing violent storm conditions in the asteriod belt at this
time. We may lose this valuable deep space communication link.
Please, be as brief as possible.
Thank you."
BRIDGE
or it's...or it's..."Hello?" "Hello operator?"
" Yes, we've lost the connection! Could you try again please?"
-"I'm sorry, but I'm afraid we've lost contact with Mars 2-4-7
at this time."
CHORUS repeat 3 times WHILE SAYING:
"Ok. Thank you very much...
I'll...I'll try again next year...next year...next year...next year..."
CHORUS INTERMEZZO
SOLO BASS-GUITAR
BRIDGE INTERMEZZO