A055237 Sums of two powers of 5.

2, 6, 10, 26, 30, 50, 126, 130, 150, 250, 626, 630, 650, 750, 1250, 3126, 3130, 3150, 3250, 3750, 6250, 15626, 15630, 15650, 15750, 16250, 18750, 31250, 78126, 78130, 78150, 78250, 78750, 81250, 93750, 156250, 390626, 390630, 390650, 390750, 391250, 393750, 406250, 468750, 781250

Offset

0,1

Links

T. D. Noe, Rows n = 0..100 of triangle, flattened

Michael Penn, Fives and squares., YouTube video, 2021.

Formula

a(n) = 5^(n-trinv(n))+5^trinv(n), where trinv(n) = floor((1+sqrt(1+8*n))/2) = A002262(n) and n-trinv(n) = A003056(n).

Regarded as a triangle T(n, k) = 5^n + 5^k, so as a sequence a(n) = 5^A002262(n) + 5^A003056(n).

Mathematica

t = 5^Range[0, 9]; Select[Union[Flatten[Table[i + j, {i, t}, {j, t}]]], # <= t[[-1]] + 1 &] (* T. D. Noe, Oct 09 2011 *)
Total/@Tuples[5^Range[0, 9], 2]//Union (* Harvey P. Dale, Jan 29 2017 *)

Prog

(Python)
from math import isqrt
def A055237(n): return 5**(a:=(k:=isqrt(m:=n<<1))+(m>k*(k+1))-1)+5**(n-1-(a*(a+1)>>1)) # Chai Wah Wu, Apr 08 2025

Crossrefs

Cf. A052216.

Sequence in context: A258143 A369290 A079713 * A057434 A333170 A217381

Adjacent sequences: A055234 A055235 A055236 * A055238 A055239 A055240

Keyword

nonn,easy,tabl

Author

Henry Bottomley, Jun 22 2000

Status

approved