This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384094 #10 Jun 18 2025 00:50:43
%S A384094 3,6,9,12,15,18,21,39,45,48,51,102,105,111,201,249,318,321,348,351,
%T A384094 501,549,1002,1005,1011,1101,1149,1761,2001,4899,5001,10002,10005,
%U A384094 10011,10101,10149,11001,14499,20001,50001,100002,100005,100011,100101,101001,110001,200001,375501,500001,1000002
%N A384094 Numbers whose square has digit sum 9 and no trailing zero.
%C A384094 All numbers of the form 10^a + 10^b + 1 (i.e., A052216+1 = 3*A237424) and of the form 10^a + 5*10^b with min(a, b) = 0 (i.e., A133472 U A199685), are in this sequence. Terms not of this form are (9, 18, 39, 45, 48, 249, 318, 321, 348, 351, 549, 1149, 1761, 4899, 10149, 14499, 375501, ...), see subsequence A384095. (Is this sequence finite? What is the next term?)
%C A384094 Is it true that no number > 1049 = A215614(6) has a square with digit sum less than 9, other than the trivial 1 and 4?
%o A384094 (PARI) select( {is_A384094(n)=n%10 && sumdigits(n^2)==9}, [1..10^5])
%Y A384094 Cf. A004159 (sum of digits of n^2), A215614 (sumdigits(n^2) = 7), A133472 (10^n + 5), A199685 (5*10^n + 1), A052216 (10^a + 10^b), A237424 ((10^a + 10^b + 1)/3).
%Y A384094 See also: A058414 (digits(n^2) in {0,1,4}).
%K A384094 nonn,base
%O A384094 1,1
%A A384094 _M. F. Hasler_, Jun 15 2025