A294076 Absolute difference between n-th stella octangula number (A007588) and the nearest perfect power (A001597).

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, 157, 35, 195, 92, 146, 15, 32, 17, 174, 134, 251, 145, 145, 263, 204, 160, 91, 230, 245, 124, 145, 337, 236, 24, 50, 26, 264, 415, 153, 234, 473, 552, 459, 182, 291

Offset: 0

Author

Felix Fröhlich, Feb 07 2018

Keywords

• nonn

Comments

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).

Links

• Wikipedia, Stella octangula number

Crossrefs

Cf. A001597, A007588.

Programs

Mathematica

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 *)

PARI

a007588(n) = n*(2*n^2-1)
is_a001597(n) = ispower(n) || n==1
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++)
a(n) = abs(a007588(n)-nearestpower(a007588(n)))