A025625 Numbers of form 5^i*10^j, with i, j >= 0.

1, 5, 10, 25, 50, 100, 125, 250, 500, 625, 1000, 1250, 2500, 3125, 5000, 6250, 10000, 12500, 15625, 25000, 31250, 50000, 62500, 78125, 100000, 125000, 156250, 250000, 312500, 390625, 500000, 625000, 781250, 1000000, 1250000, 1562500, 1953125

Offset: 1

Author

David W. Wilson

Keywords

• easy
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A000351 and A011557.

Programs

Maple

N:= 10^8: # for all terms <= N
sort([seq(seq(5^i*10^j, j=0..floor(log[10](N/5^i))),i=0..floor(log[5](N)))]); # Robert Israel, Nov 19 2019

Mathematica

Block[{a = 5, b = 10, n = 10^7}, Sort@ Flatten@ Table[a^p * b^q, {p, 0, Log[a, n]}, {q, 0, Log[b, n/(a^p)]}]] (* Michael De Vlieger, Nov 19 2019 *)

PARI

list(lim)=my(v=List(), N); for(n=0, logint(lim\=1, 10), N=10^n; while(N<=lim, listput(v, N); N*=5)); Set(v) \\ Charles R Greathouse IV, Jan 10 2018

Formula

Sum_{n>=1} 1/a(n) = (5*10)/((5-1)*(10-1)) = 25/18. - Amiram Eldar, Sep 25 2020

a(n) ~ exp(sqrt(2*log(5)*log(10)*n)) / sqrt(50). - Vaclav Kotesovec, Sep 25 2020

a(n) = 5^A025655(n) * 10^A025687(n). - R. J. Mathar, Jul 06 2025