A038491 Sums of 3 distinct powers of 11.

133, 1343, 1453, 1463, 14653, 14763, 14773, 15973, 15983, 16093, 161063, 161173, 161183, 162383, 162393, 162503, 175693, 175703, 175813, 177023, 1771573, 1771683, 1771693, 1772893, 1772903, 1773013, 1786203, 1786213, 1786323

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Base-11 interpretation of A038445.

Cf. A000217, A000292.

Programs

Maple

seq(seq(seq(11^a+11^b+11^c,c=0..b-1),b=1..a-1),a=2..10); # Robert Israel, Dec 23 2016

Mathematica

TakeWhile[#, # <= 1800000 &] &@ Sort@ Map[Total, 11^Subsets[Range[0, 8], {3}]] (* Michael De Vlieger, Dec 23 2016 *)

Python

from math import isqrt, comb
from sympy import integer_nthroot
def A038491(n): return 11**((r:=n-1-comb((m:=integer_nthroot(6*n,3)[0])+(t:=(n>comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2))+11**((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+11**(m+t+1) # Chai Wah Wu, Apr 05 2025

Formula

a(A000292(m+1)+k) = a(A000292(m)+k) + 10*11^(m+2) for 0<=k<=A000217(m). - Robert Israel, Dec 23 2016