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Decimal expansion of 5^n contains no pair of consecutive equal digits (probably finite).
1

%I #16 Mar 07 2024 16:41:09

%S 0,1,2,3,4,5,6,7,8,9,10,14,15,16,17,18,19,20,21,22,27,28,29,32

%N Decimal expansion of 5^n contains no pair of consecutive equal digits (probably finite).

%C No further terms up to 3000. - _Harvey P. Dale_, May 11 2011

%C No further terms up to 80000. - _Ivan N. Ianakiev_, Aug 31 2019

%e 5^32 = 23283064365386962890625.

%p q:= n-> (s-> andmap(i-> s[i]<>s[i+1], [$1..length(s)-1]))(""||(5^n)):

%p select(q, [$0..200])[]; # _Alois P. Heinz_, Mar 07 2024

%t Select[Range[0,3000],And@@(First[#]!=Last[#]&/@Partition[ IntegerDigits[ 5^#],2,1])&] (* _Harvey P. Dale_, May 11 2011 *)

%t Select[Range[0,40],SequenceCount[IntegerDigits[5^#],{x_,x_}]==0&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 12 2020 *)

%Y Cf. A008839, A046263, A046271.

%K nonn,base

%O 0,3

%A _Patrick De Geest_, Sep 15 1999