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

1,2

Comments

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

Links

Table of n, a(n) for n=1..32.

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

Example

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

Mathematica

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

Crossrefs

Cf. A000217, A014263, A117978, A347475.

Sequence in context: A084807 A367975 A184032 * A361855 A380073 A047630

Adjacent sequences: A383936 A383937 A383938 * A383940 A383941 A383942

Keyword

nonn,base

Author

Shyam Sunder Gupta, Aug 18 2025

Status

approved