A214451 Arithmetic mean of next a(n) successive squares of positive integers is prime.
5, 11, 29, 43, 17, 131, 13, 7, 17, 7, 53, 19, 25, 35, 65, 59, 17, 35, 113, 43, 25, 35, 5, 7, 5, 11, 89, 23, 17, 35, 29, 43, 5, 31, 109, 71, 65, 7, 41, 31, 61, 35, 25, 107, 25, 11, 41, 47, 25, 175, 41, 35, 29, 23, 17, 43, 197, 91, 13, 95, 17, 47, 5, 7, 25, 11
Offset: 1
Keywords
Examples
(1+4+9+16+25)/5 = 11, so a(1)=5. The next set of successive squares with prime arithmetic mean: (6^2 + 7^2 + ... + 16^2)/11=131, so a(2)=11.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
r:= 0: for n from 1 to 100 do t:= 0: for j from r+1 do t:= t + j^2; s:= t/(j-r); if s::integer and isprime(s) then A[n]:= j-r; r:= j; break fi od; od: seq(A[i],i=1..100); # Robert Israel, May 02 2018
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