A176765 -id:A176765 - cp's OEIS frontend

A176764 Smallest power of 4 whose decimal expansion contains n.

1024, 1, 256, 16384, 4, 256, 16, 1048576, 16384, 4096, 1024, 1099511627776, 1125899906842624, 1180591620717411303424, 262144, 288230376151711744, 16, 17179869184, 1073741824, 4194304, 72057594037927936, 262144, 4722366482869645213696

Offset: 0

Jonathan Vos Post, Apr 25 2010

This is to 4 as A176763 is to 3 and as A030001 is to 2.

			a(1) = 1 because 4^0 = 1 has "1" as a substring (not a proper substring, though).
a(2) = 256 because 4^4 = 256 has "2" as a substring.
a(3) = 16384 because 4^7 = 16384 has "3" as a substring.

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A000302, A030001, A176763, A176765-A176773.

A176764[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[4^++k], IntegerString[n]]]; 4^k]; Array[A176764, 50, 0] (* Paolo Xausa, Apr 03 2024 *)

a(n) = MIN{A000302(i) such that n in decimal representation is a substring of A000302(i)}.

a(n) = 4^A062521(n). - Michel Marcus, Sep 30 2014

Corrected and extended by Sean A. Irvine and Jon E. Schoenfield, May 05 2010

a(0) prepended by Paolo Xausa, Apr 03 2024

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

Original entry on oeis.org

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

Offset: 2

Jonathan Vos Post, Feb 26 2011

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

			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.

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

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

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

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

cp's OEIS Frontend

A176764 Smallest power of 4 whose decimal expansion contains n.

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