A383939 Numbers k such that k and the k-th triangular number T(k) = k*(k+1)/2 have only even digits.

0, 28, 40, 64, 400, 2828, 4000, 4064, 6428, 22840, 24028, 40000, 202428, 240028, 400000, 2040040, 2400028, 4000000, 6422840, 6428064, 6646624, 20044064, 20202080, 20400040, 20406080, 24000028, 40000000, 66400064, 200042428, 204000040, 228406080, 240000028

Offset: 1

Author

Shyam Sunder Gupta, Aug 18 2025

Keywords

• nonn
• base
• new

Comments

The sequence also contains the infinite subsequence 4*10^n for n >= 1.

Examples

			64 is a term since it and T(64) = 2080 both have only even digits.
		

Links

• Shyam Sunder Gupta, Triangular Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 3, 82-125.

Crossrefs

Cf. A000217, A014263, A117978, A347475.

Programs

Mathematica

q[k_] := And @@ (AllTrue[IntegerDigits[#], EvenQ] & /@ {k, k*(k+1)/2}); Select[Range[0, 4*10^6], q] (* Amiram Eldar, Aug 18 2025 *)