A239941 Primes p which are floor of Root-mean-cube (RMC) of prime(n), prime(n+1) and prime(n+2).
7, 53, 89, 223, 257, 1097, 6823, 10181, 12149, 14783, 15527, 20063, 22027, 29917, 30539, 40519, 42491, 43261, 50543, 51511, 57727, 65063, 68639, 72103, 97453, 99391, 100693, 108463, 108893, 110281, 111581, 113363, 116719, 149623, 153407, 154211, 155821, 193057
Offset: 1
Keywords
Examples
11, 13 and 17 are consecutive primes: sqrt(( 11^3 + 13^3 + 17^3)/3) = 53.044...: floor(53.044...) = 53, which is prime and appears in the sequence. 31, 37 and 41 are consecutive primes: sqrt(( 31^3 + 37^3 + 41^3)/3) = 223.13...: floor(223.13...) = 223, which is prime and appears in the sequence.
Links
- Georg Fischer, Table of n, a(n) for n = 1..1745 (first 429 terms from K. D. Bajpai)
Programs
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Maple
select(isprime, {seq(floor(sqrt(add(ithprime(n+i)^3, i=0..2)/3)), n=1..1000)})[]; # corrected by Georg Fischer, Sep 27 2024