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Search: id:A084289
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| A084289 |
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Primes p such that arithmetical mean of p and nextp[p] is a true prime power from A025475. |
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| 3, 7, 61, 79, 619, 1669, 4093, 822631, 1324783, 2411797, 2588869, 2778877, 3243589, 3636631, 3736477, 5527189, 6115717, 6405943, 8720191, 9005989, 12752029, 16056031, 16589317, 18087991, 21743551, 25230511, 29343871, 34586131
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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Primes p[j] so that (p[j]+p[j+1])/2=q[m]^w, where q[m] is a prime.
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EXAMPLE
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n=p[9750374]=174689077, bextprime=174689101, mean=174689089=13217^2, a prime power.
Arithmetic mean of two consecutive primes is never prime,
while between p and nextp[p] prime-powers occur;
here these prime-powers are in the middle of gap: p+d/2=q^w;
prime-power is most often square and very rarely occurs more than once [see A053706]
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MAPLE
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fi[x_] := FactorInteger[x] ff[x_] := Length[FactorInteger[x]] Do[s=(Prime[n]+Prime[n+1])/2; s1=ff[s]; If[Equal[s1, 1], Print[{n, p=Prime[n], s, fi[s], s-p, s1}]], {n, 1, 10000000}]
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CROSSREFS
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Cf. A053706, A000961, A025475.
Sequence in context: A131652 A164895 A046859 this_sequence A077703 A134705 A110433
Adjacent sequences: A084286 A084287 A084288 this_sequence A084290 A084291 A084292
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), May 26 2003
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