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A277441 Least number k such that k^2 can be obtained from k by inserting n internal (but not necessarily contiguous) digits. 1

%I

%S 0,10,95,950,9500,89476,894760,8946105,89448001,894438005,8944300005,

%T 89442827780,894427300005,8944273000005,89442720000005,

%U 894427196000005,8944271912400005,89442719120000005,894427191000000005,8944271910000000005,89442719100000000005,894427191000000000005

%N Least number k such that k^2 can be obtained from k by inserting n internal (but not necessarily contiguous) digits.

%C A subsequence of A046851.

%e a(2) = 95 as 95 is the least number that needs two internal digits inserted to become its square, i.e., 95 squared is 9(02)5.

%p P:=proc(q) local a,b,d,j,k,n,ok,t; t:=1; print(0);

%p for n from 1 to q do for k from t to q do if ilog10(k^2)=ilog10(k)+n then

%p if (k^2 mod 10)=(k mod 10) and trunc(k^2/10^(ilog10(k^2)))=trunc(k/10^(ilog10(k))) then

%p a:=convert(k,base,10); b:=convert(k^2,base,10); ok:=1; d:=1;

%p for j from 2 to nops(a)-1 do while d<nops(b)-1 do d:=d+1; if a[j]=b[d] then break; fi; od;

%p if d=nops(b)-1 and j<=nops(a)-1 then ok:=0; break; fi; od;

%p if ok=1 then t:=k; print(k); break; fi; fi; fi; od; od; end: P(10^15); # _Paolo P. Lava_, Oct 20 2016

%Y Cf. A046851, A277442.

%K nonn,base

%O 0,2

%A _Ivan N. Ianakiev_, Oct 15 2016

%E More terms from _Paolo P. Lava_, Oct 20 2016

%E a(13)-a(21) from _Giovanni Resta_, Jul 06 2019

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Last modified October 3 17:45 EDT 2022. Contains 357237 sequences. (Running on oeis4.)