A186774 Smallest power of n whose decimal expansion contains n+1, or 0 if no such number exists.

32, 243, 256, 625, 7776, 16807, 4096, 31381059609, 0, 121, 79496847203390844133441536, 51185893014090757, 155568095557812224, 22168378200531005859375, 17592186044416, 118587876497, 11019960576, 42052983462257059

Offset: 2

Author

Jonathan Vos Post, Feb 26 2011

Keywords

• nonn
• base
• easy

Comments

More precisely: smallest power of n (with positive integer exponent) whose decimal expansion contains n+1 as a substring of consecutive decimal digits. This is A[n,n+1], the diagonal above the trivial main diagonal of the array A[k,n] = Smallest power of k whose decimal expansion contains n.

The k=2 row A[2,n] = A030001.

The k=3 row A[3,n] = A176763.

The k=4 row A[4,n] = A176764.

The k=5 row A[5,n] = A176765...

a(10^k+1) = (10^k+1)^2 for k > 0. - Chai Wah Wu, Feb 13 2017

Examples

			a(2) = 32 = A030001(3) = smallest power of 2 whose decimal expansion contains 3.
a(3) = 243 = A176763(4) = smallest power of 3 whose decimal expansion contains 4.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..1999

Crossrefs

Cf. A018856, A063565, A030001, A176763-A176773.

Programs

Maple

a:= proc(n) local t, k;
      if type(simplify(log[10](n)), integer) then 0
    else t:= cat(n+1);
         for k from 2 while searchtext(t, cat(n^k))=0
         do od; n^k
      fi
    end:
seq(a(n), n=2..40);  # Alois P. Heinz, Feb 26 2011

Python

def A186774(n):
    if sum(int(d) for d in str(n)) == 1:
        return 0
    sn, k = str(n+1), 1
    while sn not in str(k):
        k *= n
    return k # Chai Wah Wu, Feb 13 2017