A038475 Sums of 3 distinct powers of 5.

31, 131, 151, 155, 631, 651, 655, 751, 755, 775, 3131, 3151, 3155, 3251, 3255, 3275, 3751, 3755, 3775, 3875, 15631, 15651, 15655, 15751, 15755, 15775, 16251, 16255, 16275, 16375, 18751, 18755, 18775, 18875, 19375, 78131, 78151, 78155, 78251, 78255, 78275, 78751

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Base 5 interpretation of A038445.

Cf. A000351, A038474, A038476, A038477.

Programs

Mathematica

Sort[Plus @@@ Subsets[5^Range[0, 7], {3}]] (* Amiram Eldar, Jul 13 2022 *)

Python

from math import isqrt, comb
from sympy import integer_nthroot
def A038475(n): return 5**((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))+5**((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+5**(m+t+1) # Chai Wah Wu, Apr 04 2025

Extensions

Offset corrected by Amiram Eldar, Jul 13 2022