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124C41
 Senior Boarder
Posts: 69 
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Can someone put me out of my misery? What's the next number in this series: 1 4 16 64 4096 ... ?
I think I've seen this one a long time ago and I think it's sneaky. It does appear on a numerical sequences website but it's a horrible trig function and this was a question to a 6th grade class.
Apologies if this is well-known, I don't usually read this ng -
Derek Wills
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paydayuscf
Senior Boarder
Posts: 79
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2^0 2^2 2^4 2^6 2^12
Why does the exponent go from 6 to 12 when it had been increasing by 2?
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jugherffere
 Expert Boarder
Posts: 84
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Well, dat's de question! If the last term had been 256 I wouldn't have insulted the readers of this ng by posing the question  |
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imported_Bojan
Senior Boarder
Posts: 78
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Well, as you know, *any* number could be the next one. But one possibility for what the question-setter has in mind is a alternating rule: multiply by 4, then square, then repeat. In which case the next 5 terms would be: 16384, 268435456, 1073741824, 1152921504606846976, 4611686018427387904.
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ciproantib
Senior Boarder
Posts: 71
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could be 4^7 (4^n, n contains no 'f'  |
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quest2006
Senior Boarder
Posts: 60
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One possible answer is, because 6 + 4 + 2 is 12 (as 4 + 2 + 0 is 6). Following this rule, the next number in the sequence would be:
2^22
Seems too twisted for my taste, though...
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jugherffere
Expert Boarder
Posts: 84
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Or, 4^0 4^1 4^2 4^3 4^6 4^12
Wouldn't that be 2^24 ?
Actually, I like that progression best, so far. The trig function Sreeram posted about MAY be what the original author intended, but for 6th grade, it seems a bit extreme! A semi-simple arithmetic progression of exponents would be more reasonable. As in the Fibonacci series, it needs a couple terms to start, then continues forever. For that matter, a Fibonacci series in the exponents would make another nice puzzle series...
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imported_Adrian
Senior Boarder
Posts: 72
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Trig function? It seems to be a progression of exponents.
1 = 2^0 4 = 2^2 16 = 2^4 64 = 2^6 4096 = 2^12
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kdavis004
Senior Boarder
Posts: 63
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I think that throwing away the signs is cheating, personally. 16 and -16 are different numbers. If you think they're the same, lend me 16 Euros, and I'll pay you back -16.
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quest_marsman
Senior Boarder
Posts: 72
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No... Err... let me double check my sanity... Hmmm, no, I still think it's 2^22
If you see it as powers of 4, then it would be 4^11 (or 2^22). The progression is: 2 (or 4) to the power of the sum of the last three exponents:
2^(12+6+4) |
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