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A111005
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Powers of the form 2*prime(n)-prime(n+1).
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0
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9, 9, 27, 25, 81, 125, 225, 225, 361, 441, 1089, 1089, 1225, 1225, 2025, 2025, 2601, 3249, 3249, 3375, 3721, 5041, 6859, 7569, 7921, 12321, 13689, 13689, 15129, 18225, 21609, 21609, 30625, 31329, 38809, 42025, 47961, 53361, 59049, 65025, 65025
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| a(n)=2*prime(n)-prime(n+1) and a(n) is a power.
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EXAMPLE
| a(20)=2*prime(478)-prime(479)=2*3391-3407=3375=15^3.
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MAPLE
| with(numtheory); egcd := proc(n) local L; L:=map(proc(z) z[2] end, ifactors(n)[2]); igcd(op(L)) end: PW:=[]: cnt:=0: for z to 1 do for j from 1 to 50000 do x:=2*ithprime(j)-ithprime(j+1); if egcd(x)>1 then cnt:=cnt+1; PW:=[op(PW), [cnt, j, x]] fi od od; PW; map(proc(z) z[3] end, PW);
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CROSSREFS
| Sequence in context: A014725 A202208 A059816 * A076089 A046000 A147378
Adjacent sequences: A111002 A111003 A111004 * A111006 A111007 A111008
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KEYWORD
| nonn
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AUTHOR
| Walter A. Kehowski (wkehowski(AT)cox.net), Oct 02 2005
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