cp's OEIS Frontend

A358034 Numbers k such that A234575(k,s) = s^2 where s = A007953(k).

%I A358034 #10 Oct 26 2022 13:40:42
%S A358034 1,113,313,331,512,1271,2065,2137,2173,2705,3291,3931,4066,4913,5832,
%T A358034 6535,6553,6571,6607,6625,6643,6661,6715,6733,6751,6805,6823,6841,
%U A358034 7715,13479,13686,15289,15577,17576,19449,19683,21898,23969,49789,49897,49969
%N A358034 Numbers k such that A234575(k,s) = s^2 where s = A007953(k).
%C A358034 Numbers k such that, if the sum of digits of k is s, the quotient and remainder on division of k by s sum to s^2.
%e A358034 a(3) = 313 is a term because the sum of digits of 313 is 7, 313 = 44*7+5, and 44+5 = 49 = 7^2.
%p A358034 filter:= proc(n) local s,q,r;
%p A358034   s:= convert(convert(n,base,10),`+`);
%p A358034 r:= n mod s;
%p A358034   q:= (n-r)/s;
%p A358034 q+r = s^2
%p A358034 end proc:
%p A358034 select(filter, [$1..10^6]);
%o A358034 (Python)
%o A358034 from itertools import count, islice
%o A358034 def A358034_gen(startvalue=1): # generator of terms >= startvalue
%o A358034     return filter(lambda n:(s:=sum(int(d) for d in str(n)))**2 == sum(divmod(n,s)),count(max(startvalue,1)))
%o A358034 A358034_list = list(islice(A358034_gen(),30)) # _Chai Wah Wu_, Oct 26 2022
%Y A358034 Cf. A007953, A234575.
%K A358034 nonn,base,fini,full
%O A358034 1,2
%A A358034 _J. M. Bergot_ and _Robert Israel_, Oct 25 2022