login
Numbers k such that decimal expansion of k^2 contains k as a substring and k does not end in 0.
8

%I #26 Apr 04 2023 15:25:34

%S 1,5,6,25,76,376,625,3792,9376,14651,90625,109376,495475,505025,

%T 890625,971582,1713526,2890625,4115964,5133355,6933808,7109376,

%U 10050125,12890625,48588526,50050025,66952741,87109376,88027284,88819024

%N Numbers k such that decimal expansion of k^2 contains k as a substring and k does not end in 0.

%C Subsequence of A018834. - _Chai Wah Wu_, Apr 04 2023

%H Giovanni Resta, <a href="/A046831/b046831.txt">Table of n, a(n) for n = 1..64</a>

%t Reap[For[n = 1, n < 10^8, n++, If[Mod[n, 10] != 0, If[StringPosition[ToString[n^2], ToString[n]] != {}, Print[n]; Sow[n]]]]][[2, 1]] (* _Jean-François Alcover_, Apr 04 2013 *)

%o (Haskell)

%o a046831 n = a046831_list !! (n-1)

%o a046831_list = filter ((> 0) . (`mod` 10)) a018834_list

%o -- _Reinhard Zumkeller_, Jul 27 2011

%o (Python)

%o from itertools import count, islice

%o def A046831_gen(startvalue=0): # generator of terms >= startvalue

%o return filter(lambda n:n%10 and str(n) in str(n**2), count(max(startvalue,0)))

%o A046831_list = list(islice(A046831_gen(),20)) # _Chai Wah Wu_, Apr 04 2023

%Y Cf. A018834, A003226, A008851.

%K nonn,base

%O 1,2

%A _David W. Wilson_