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

1, 113, 313, 331, 512, 1271, 2065, 2137, 2173, 2705, 3291, 3931, 4066, 4913, 5832, 6535, 6553, 6571, 6607, 6625, 6643, 6661, 6715, 6733, 6751, 6805, 6823, 6841, 7715, 13479, 13686, 15289, 15577, 17576, 19449, 19683, 21898, 23969, 49789, 49897, 49969

Offset: 1

Author

J. M. Bergot and Robert Israel, Oct 25 2022

Keywords

• nonn
• base
• fini
• full

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A007953, A234575.

Programs

Maple

filter:= proc(n) local s,q,r;
  s:= convert(convert(n,base,10),`+`);
r:= n mod s;
  q:= (n-r)/s;
q+r = s^2
end proc:
select(filter, [$1..10^6]);

Python

from itertools import count, islice
def A358034_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:(s:=sum(int(d) for d in str(n)))**2 == sum(divmod(n,s)),count(max(startvalue,1)))
A358034_list = list(islice(A358034_gen(),30)) # Chai Wah Wu, Oct 26 2022