A270696 Perfect powers that are the average of two consecutive primes.
4, 9, 64, 81, 144, 225, 324, 441, 625, 1089, 1681, 1728, 2601, 3600, 4096, 5184, 6084, 8464, 12544, 13689, 16641, 17576, 19044, 19600, 21952, 25281, 27225, 28224, 29584, 36864, 38025, 39204, 45369, 46656, 47524, 51984, 56169, 74529, 87025, 88804, 91809, 92416, 95481
Offset: 1
Keywords
Examples
1728 is a term because 1728 = 12^3 = (1723 + 1733)/2.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Select[Mean/@Partition[Prime[Range[10000]],2,1],GCD@@FactorInteger[#][[All,2]]>1&] (* Harvey P. Dale, Jun 22 2022 *)
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PARI
for(n=2, 1e5, if((nextprime(n) - n) == (n - precprime(n)) && ispower(n), print1(n, ", ")));
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PARI
list(lim)=my(v=List(),t); forprime(e=2,logint(lim\=1,2), for(m=2,sqrtnint(lim,e), t=m^e; if(t-precprime(t)==nextprime(t)-t, listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Mar 21 2016
Comments