A240339 Primes p which are floor of Root-Mean-Cube (RMC) of prime(n) and prime(n+1).
59, 97, 1321, 1621, 2539, 3511, 4339, 4889, 5591, 6491, 6917, 9419, 10289, 11689, 16381, 18719, 19441, 23053, 23567, 28499, 41051, 47143, 64661, 65203, 67939, 71023, 82493, 89107, 94999, 98927, 106087, 114941, 117281, 120823, 135647, 139361, 144289, 154799
Offset: 1
Keywords
Examples
13 and 17 are consecutive primes: sqrt((13^3 + 17^3)/2) = 59.62382073: floor(59.62382073)= 59, which is prime and appears in the sequence. 19 and 23 are consecutive primes: sqrt((19^3 + 23^3)/2) = 97.53460923: floor(97.53460923)= 97, which is prime and appears in the sequence.
Links
- Georg Fischer, Table of n, a(n) for n = 1..1700 (first 357 terms from K. D. Bajpai)
Programs
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Maple
select(isprime, {seq(floor(sqrt((ithprime(n)^3 + ithprime(n+1)^3)/2)),n=1..1000)}); # corrected by Georg Fischer, Sep 27 2024 -
Mathematica
Select[Floor[Sqrt[Mean[#]]]&/@(Partition[Prime[Range[600]],2,1]^3), PrimeQ] (* Harvey P. Dale, Sep 24 2014 *)