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 A068127 Triangular numbers with sum of digits = 3. 7
 3, 21, 120, 210, 300, 10011, 20100, 2001000, 200010000, 20000100000, 2000001000000, 200000010000000, 20000000100000000, 2000000001000000000, 200000000010000000000, 20000000000100000000000, 2000000000001000000000000, 200000000000010000000000000, 20000000000000100000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence is unbounded, as the (2*10^k)-th triangular number is a term. LINKS Michael S. Branicky, Table of n, a(n) for n = 1..504 MATHEMATICA t = {}; Do[tri = n*(n+1)/2; If[Total[IntegerDigits[tri, 10]] == 3, AppendTo[t, tri]], {n, 1000000}]; t (* T. D. Noe, Jun 05 2012 *) Select[Accumulate[Range[2*10^6]], Total[IntegerDigits[#]]==3&] (* Harvey P. Dale, Jun 22 2021 *) Sort @ Select[Plus @@@ (10^Select[Tuples[Range[0, 29], 3], Min[Differences[#]] >= 0 &]), IntegerQ[Sqrt[8*# + 1]] &] (* Amiram Eldar, May 19 2022 *) PROG (Python) from math import isqrt from itertools import count, islice def istri(n): return (lambda x: x == isqrt(x)**2)(8*n+1) def agen(): yield from filter(istri, (10**i + 10**j + 10**k for i in count(0) for j in range(i+1) for k in range(j+1))) print(list(islice(agen(), 20))) # Michael S. Branicky, May 14 2022 CROSSREFS Cf. A000217, A004157, A052217. Sequence in context: A046727 A283421 A117512 * A247247 A322185 A171137 Adjacent sequences: A068124 A068125 A068126 * A068128 A068129 A068130 KEYWORD base,easy,nonn AUTHOR Amarnath Murthy, Feb 21 2002 EXTENSIONS More terms from Sascha Kurz, Mar 06 2002 One additional term (a(12)) from Harvey P. Dale, May 14 2022 More terms and offset changed to 1 from Michael S. Branicky, May 14 2022 STATUS approved

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Last modified December 2 09:50 EST 2023. Contains 367517 sequences. (Running on oeis4.)