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A139021
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a(0)=2. a(n) = smallest prime > a(n-1) such that (Sum_{k=0..n} a(k)) is a power of a prime.
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3
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2, 3, 11, 13, 227, 307, 461, 463, 2609, 2683, 58757, 58831, 137777, 138007, 17179469033, 17179470433, 240518567327, 240518567479, 19807040628566083882989513161, 19807040628566083882989513433, 324478939577169594614874645075239, 324478939577169594614874645093097
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OFFSET
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0,1
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LINKS
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EXAMPLE
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The corresponding prime powers are 2 + 3 = 5^1, 2 + 3 + 11 = 2^4, 2 + 3 + 11 + 13 = 29^1, etc.
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MAPLE
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a := [2, 3] ; while true do as := add(i, i=a) ; p := nextprime(op(-1, a)) ; while nops(numtheory[factorset](p+as)) > 1 do p := nextprime(p) ; od; a := [op(a), p] ; print(a) ; od: # R. J. Mathar, Apr 28 2008
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PROG
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(PARI) { printA139021() = my(a=2, s=2); print1(2, ", "); for(n=2, 100, if( s%2==0, until(isprimepower(s+a), a=nextprime(a+1)), t=log(s+a)\log(2) + 1; while( !ispseudoprime(2^t-s), t++); a=2^t-s; ); s+=a; print1(a, ", "); ); } /* Max Alekseyev, Oct 17 2015 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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