A038474 Sums of two distinct powers of 5.

6, 26, 30, 126, 130, 150, 626, 630, 650, 750, 3126, 3130, 3150, 3250, 3750, 15626, 15630, 15650, 15750, 16250, 18750, 78126, 78130, 78150, 78250, 78750, 81250, 93750, 390626, 390630, 390650, 390750, 391250, 393750, 406250, 468750, 1953126, 1953130, 1953150

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 A038444.

Cf. A000351, A038475, A038476, A038477.

Programs

Mathematica

Union[Total/@Subsets[5^Range[0, 15], {2}]] (* Harvey P. Dale, Jan 06 2011 *)

Python

from itertools import combinations, count, takewhile
def aupto(lim):
  p = takewhile(lambda x: x<= lim, (5**i for i in count(0)))
  t = (sum(c) for c in combinations(p, 2))
  return sorted(filter(lambda x: x <= lim, t))
print(aupto(10**6)) # Michael S. Branicky, Jun 26 2021

Python

from math import isqrt
def A038474(n): return 5**(m:=isqrt(n<<3)+1>>1)+5**(n-1-(m*(m-1)>>1)) # Chai Wah Wu, Apr 04 2025

Extensions

Offset changed to 1 and a(37) and beyond from Michael S. Branicky, Jun 26 2021