A246753 Triangular numbers with strictly increasing product of digits.

1, 3, 6, 28, 36, 45, 55, 66, 78, 276, 378, 496, 595, 1596, 2485, 2775, 3486, 4656, 5565, 5778, 5995, 8778, 25878, 26796, 35778, 47586, 47895, 58996, 196878, 277885, 359976, 378885, 448878, 468996, 569778, 786885, 887778, 2489796, 2797795, 3667986, 3689686, 3887866

Offset: 1

Author

K. D. Bajpai, Sep 02 2014

Keywords

• nonn
• base

Examples

			a(4) = 28 = 7 * (7 + 1) / 2, which is 7th triangular number with product of digits = 2 * 8 = 16.  a(5) = 36 = 8 * (8 + 1) / 2, which is 8th triangular number with product of digits = 3 *6 = 18. Since  18 > 16, 28 and 36 are in list.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..159

Crossrefs

Cf. A000217, A007954, A230041.

Programs

Mathematica

A246753 = {}; t = 0; Do[k = n*(n + 1)/2; s = Apply[Times, IntegerDigits[k]];If[s > t, t = s; AppendTo[A246753, k]], {n, 1, 100}]; A246753
DeleteDuplicates[{#,Times@@IntegerDigits[#]}&/@Accumulate[Range[3000]],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* Harvey P. Dale, Oct 29 2024 *)