A247021 Triangular numbers composed of only digits with line segments or both line segments and curves {1, 2, 4, 5, 7}.

1, 15, 21, 45, 55, 171, 741, 1225, 1275, 1711, 2145, 2211, 2415, 2775, 5151, 11175, 15225, 21115, 22155, 25425, 44551, 45451, 72771, 77421, 112575, 121771, 124251, 125751, 151525, 211575, 221445, 222111, 224115, 227475, 254541, 255255, 417241, 451725, 551775, 577275

Offset: 1

Author

K. D. Bajpai, Sep 09 2014

Keywords

• nonn
• base
• less

Comments

Intersection of A000217 and A082741.

Every term is congruent to 1 mod 10 or 5 mod 10. - Derek Orr, Sep 19 2014

Examples

			1275 is a term because 1275 = 50 * (50 + 1) / 2, is a triangular number composed of digits 1, 2, 7 and 5.
2145 is a term because 2145 = 65 * (65 + 1) / 2, is a triangular number composed of digits 1, 2, 4 and 5.
a(38) = 451725 is the first occurrence of triangular number using each digit 1, 2, 4, 5 or 7 at least once.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..6912

Crossrefs

Cf. A000217, A028373, A028374, A082741, A119033.

Programs

Mathematica

A247021 = {}; Do[t = n*(n + 1)/2; If[Intersection[IntegerDigits[t], {0, 3, 6, 8, 9}] == {}, AppendTo[A247021, t]], {n, 1000}]; A247021
Select[Accumulate[Range[1500]],SubsetQ[{1,2,4,5,7}, IntegerDigits[#]]&] (* Harvey P. Dale, May 20 2025 *)

Python

for n in range(10**3):
  s = str(int(n*(n+1)/2))
  if not (s.count('0') + s.count('3') + s.count('6') + s.count('8') + s.count('9')):
    print(int(s), end=', ') # Derek Orr, Sep 19 2014