|
%I #11 Mar 04 2018 23:41:19
%S 1,0,2,2,1,2,15,3,8,5,35,50,37,25,2,11,16,8,18,10,104,5,42,25,68,104,
%T 157,35,195,92,146,15,32,17,174,134,251,145,145,263,204,160,91,230,
%U 245,124,145,337,236,24,50,26,264,415,153,234,473,552,459,182,291
%N Absolute difference between n-th stella octangula number (A007588) and the nearest perfect power (A001597).
%C There are only two square stella octangula numbers, namely those corresponding to n = 1 and n = 169, so a(1) = 0 and a(169) = 0 (cf. Wikipedia link).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Stella_octangula_number">Stella octangula number</a>
%t f[n_, i_: 1] := Block[{k = n, j = If[i == 1, 1, -1]}, While[Nor[k == 1, GCD @@ FactorInteger[k][[All, 2]] > 1], k = k + j]; k]; {1}~Join~Array[Min@ Abs@ {# - f[#], f[#, 0] - #} &[# (2 #^2 - 1)] &, 60] (* _Michael De Vlieger_, Feb 21 2018 *)
%o (PARI) a007588(n) = n*(2*n^2-1)
%o is_a001597(n) = ispower(n) || n==1
%o nearestpower(n) = my(x=0); while(1, if(x < n, if(is_a001597(n-x), return(n-x), if(is_a001597(n+x), return(n+x))), if(is_a001597(n+x), return(n+x))); x++)
%o a(n) = abs(a007588(n)-nearestpower(a007588(n)))
%Y Cf. A001597, A007588.
%K nonn
%O 0,3
%A _Felix Fröhlich_, Feb 07 2018
|
