A375824 Triangular numbers whose sum of digits is 9.

36, 45, 153, 171, 351, 630, 1035, 1431, 2016, 3240, 3321, 4005, 8001, 10440, 13041, 13203, 16110, 21321, 23220, 25200, 101025, 105111, 114003, 222111, 320400, 321201, 1010331, 1241100, 1313010, 1400301, 2013021, 2031120, 2410110, 4020030, 10006101, 11203011, 20012301, 32004000, 32012001, 33020001

Offset

1,1

Comments

Infinite subsequences include 2 * 10^(2*k) + 13 * 10^k + 21, 2 * 10^(2*k) + 31 * 10^k + 120, 32 * 10^(2*k) + 4 * 10^k, and 32 * 10^(2*k) + 12 * 10^k + 1.

Conjecture: the last term not of one of those subsequences is a(53) = 210010000005.

Links

Robert Israel, Table of n, a(n) for n = 1..95

Example

a(4) = 153 is a term because 153 = 17 * 18/2 is a triangular number and 1 + 5 + 3 = 9.

Maple

F:= proc(d, s) option remember;
# d-digit numbers with sum of digits s
      local R, i;
      R:= {};
      for i from 0 to min(s, 9) do
        R:= R union map(t -> 10*t+i, procname(d-1, s-i))
      od;
      R
end proc:
F(1, 0):= {}:
for i from 1 to 9 do F(1, i):= {i} od:
sort(convert(`union`(seq(select(t -> issqr(1+8*t), F(d, 9)), d=1..12)), list));

Mathematica

Select[Range[10000](Range[10000]+1)/2, DigitSum[#]==9 &] (* Stefano Spezia, Sep 01 2024 *)

Prog

(PARI) select(x->(sumdigits(x)==9), vector(10000, n, n*(n+1)/2)) \\ Michel Marcus, Aug 31 2024

Crossrefs

Intersection of A000217 and A052223. Contained in A117404 and A076713.

Sequence in context: A048034 A195528 A144291 * A068143 A264961 A188630

Adjacent sequences: A375816 A375817 A375820 * A375825 A375826 A375827

Keyword

nonn,base,new

Author

Robert Israel, Aug 30 2024

Status

approved