A256434 Characteristic function of icosahedral numbers.

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

0

Comments

Icosahedral numbers are of the form m*(5*m^2 - 5*m + 2)/2.

Links

Antti Karttunen, Table of n, a(n) for n = 0..104160

Index entries for characteristic functions

Formula

For n > 0, a(n) = floor(t(n) - 1/(45 * t(n)) + 1/3) - floor(t(n-1) - 1/(45 * t(n-1)) + 1/3), where t(n) = ( sqrt(135*n^2-40*n+3)/(15^(3/2)) + (27*n-4)/135 )^(1/3).

For n>0, a(n) = 1 if n==m*(5*m*(m-1)+2)/2 and a(n) = 0 otherwise where m = floor((2*n/5)^(1/3))+1. - Chai Wah Wu, Oct 02 2025

Mathematica

With[{icos=Table[m (5m^2-5m+2)/2, {m, 0, 20}]}, Table[If[MemberQ[icos, n], 1, 0], {n, 0, 150}]] (* Harvey P. Dale, May 01 2026 *)

Prog

(PARI)
A006564(n) = (5*n^2*(n-1)/2+n); \\ From A006564
A256434(n) = { my(i=0); while(A006564(i) < n, i++); return(A006564(i) == n); }; \\ Antti Karttunen, Aug 05 2018
(Python)
from sympy import integer_nthroot
def A256434(n): return int((m:=integer_nthroot((k:=n<<1)//5, 3)[0]+1)*(5*m*(m-1)+2)==k) if n else 1 # Chai Wah Wu, Oct 02 2025

Crossrefs

Cf. A006564 (icosahedral numbers).

Cf. also A023533, A010057, A256432, A256433.

Sequence in context: A016423 A016360 A016412 * A247133 A186742 A016365

Adjacent sequences: A256431 A256432 A256433 * A256435 A256436 A256437

Keyword

nonn

Author

Mikael Aaltonen, Mar 28 2015

Extensions

More terms from Antti Karttunen, Aug 05 2018

Status

approved