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A110996
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Powers equal to (sum of first n primes) plus 1.
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0
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OFFSET
| 1,1
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COMMENTS
| I have checked for powers out to the 250000th prime and the last element found is at the 6420th prime, 64067. It is interesting to note that the only powers so far are squares. Finding a higher power would be interesting.
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FORMULA
| a(n)=sum(prime(j), j=1..N_n) and a(n) is a power.
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EXAMPLE
| a(1)=441 since sum(primes<=59)=440 and 441=21^2.
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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: s := proc(n) option remember; local p; if n=1 then [1, 2] else [n, s(n-1)[2]+ithprime(n)] fi end; t := proc(n) option remember; [n, s(n)[2]+1] fi end; PW:=[]; for z to 1 do for j from 1 to 250000 do if egcd(t(j)[2])>1 then PW:=[op(PW), t(j)] fi od od; PW;
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CROSSREFS
| Cf. A007504, A110979.
Sequence in context: A206467 A189278 A151656 * A013769 A013899 A075268
Adjacent sequences: A110993 A110994 A110995 * A110997 A110998 A110999
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KEYWORD
| nonn
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AUTHOR
| Walter A. Kehowski (wkehowski(AT)cox.net), Sep 30 2005
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