A069693
Triangular numbers with either no internal digits or all internal digits are 0.
Original entry on oeis.org
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 300, 406, 703, 903, 3003, 4005, 8001
Offset: 1
The internal digits of 3003 are "00", which are both 0. 15 has no internal digits.
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Do[ If[ Union[ Drop[ RotateLeft[ IntegerDigits[n(n + 1)/2]], -2]] == {0}, Print[n(n + 1)/2]], {n, 14, 2 10^6}]
A069695
Triangular numbers with internal digits 3.
Original entry on oeis.org
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 136, 231, 435, 630, 333336
Offset: 1
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Do[ If[ Union[ Drop[ RotateLeft[ IntegerDigits[n(n + 1)/2]], -2]] == {3}, Print[n(n + 1)/2]], {n, 14, 2 10^6}]
A069694
Triangular numbers with internal digits 2.
Original entry on oeis.org
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 120, 325, 528, 820, 1225
Offset: 1
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Do[ If[ Union[ Drop[ RotateLeft[ IntegerDigits[n(n + 1)/2]], -2]] == {2}, Print[n(n + 1)/2]], {n, 14, 2 10^6}]
A069696
Triangular numbers with internal digits 4.
Original entry on oeis.org
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 741, 946, 6441, 544446
Offset: 1
A069697
Triangular numbers with internal digits 5.
Original entry on oeis.org
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 153, 253, 351, 2556, 6555
Offset: 1
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Do[ If[ Union[ Drop[ RotateLeft[ IntegerDigits[n(n + 1)/2]], -2]] == {5}, Print[n(n + 1)/2]], {n, 14, 2 10^6}]
Select[Accumulate[Range[0,300]],IntegerLength[#]<3||Union[Most[Rest[IntegerDigits[#]]]]=={5}&] (* Harvey P. Dale, Aug 13 2025 *)
A069698
Triangular numbers with internal digits 6.
Original entry on oeis.org
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 465, 561, 666, 861, 46665, 5666661
Offset: 1
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Do[ If[ Union[ Drop[ RotateLeft[ IntegerDigits[n(n + 1)/2]], -2]] == {6}, Print[n(n + 1)/2]], {n, 14, 2 10^6}]
Corrected by Mark Hudson (mrmarkhudson(AT)hotmail.com), Aug 25 2004
A069699
Triangular numbers with internal digits 7.
Original entry on oeis.org
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 171, 276, 378, 1770, 2775, 5778, 8778
Offset: 1
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Do[ If[ Union[ Drop[ RotateLeft[ IntegerDigits[n(n + 1)/2]], -2]] == {6}, Print[n(n + 1)/2]], {n, 14, 2 10^6}]
Showing 1-7 of 7 results.
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