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A375824
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Triangular numbers whose sum of digits is 9.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(4) = 153 is a term because 153 = 17 * 18/2 is a triangular number and 1 + 5 + 3 = 9.
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MAPLE
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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));
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MATHEMATICA
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Select[Range[10000](Range[10000]+1)/2, DigitSum[#]==9 &] (* Stefano Spezia, Sep 01 2024 *)
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PROG
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(PARI) select(x->(sumdigits(x)==9), vector(10000, n, n*(n+1)/2)) \\ Michel Marcus, Aug 31 2024
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CROSSREFS
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KEYWORD
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nonn,base,new
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AUTHOR
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STATUS
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approved
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