A140288 The least n-digit multiple of 5^n using the decimal digits {1, 2, 3, 4, 5} exclusively.
5, 25, 125, 3125, 53125, 453125, 4453125, 14453125, 314453125, 2314453125, 22314453125, 122314453125, 4122314453125, 44122314453125, 444122314453125, 4444122314453125, 54444122314453125, 254444122314453125, 1254444122314453125, 21254444122314453125
Offset: 1
Examples
a(5) = 53125 = 17 * 5^5.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000
Programs
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PARI
lista(nn) = {v = vector(nn); v[1] = 5; for(k = 2, nn, j = 1; while((j*10^(k-1) + v[k-1]) % 5^k > 0, j++); v[k] = j*10^(k-1) + v[k-1]); for(k = 1, nn, print1(v[k], ", "));} \\ Jinyuan Wang, Aug 27 2019
Formula
To obtain the (n+1)-th term, write the n-th term as k * 5^n. Multiply k by a multiple of 2^n to get a multiple of 5. Add the multiplicator of 2^n to the left of the n-th term.
Extensions
More terms from Alois P. Heinz, Apr 05 2017