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

0,3

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

Table of n, a(n) for n=0..60.

Wikipedia, Stella octangula number

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 *)

Prog

(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)))

Crossrefs

Cf. A001597, A007588.

Sequence in context: A364492 A124839 A336846 * A334508 A364493 A117046

Adjacent sequences: A294073 A294074 A294075 * A294077 A294078 A294079

Keyword

nonn

Author

Felix Fröhlich, Feb 07 2018

Status

approved