A350990 Triangular numbers that are palindromes in base 3.

0, 1, 10, 28, 91, 820, 7381, 65341, 66430, 597871, 1633528, 5380840, 48339028, 48427561, 139386556, 435848050, 1178284240, 3529890253, 3922632451, 32614707700, 35296517971, 35303692060, 101891588176, 292358957446, 295883935480, 317733228541, 859413596320, 2649105942220

Offset

1,3

Comments

This sequence is infinite since A000217((3^k-1)/2) is a term for all k >= 0 (Trigg, 1971).

Links

Amiram Eldar, Table of n, a(n) for n = 1..50

Charles W. Trigg, Problem 3413, Problem Department, School Science and Mathematics, Vol. 71, No. 9 (1971), p. 843; Solution to Problem 3413, by Bob Prielipp, Vol. 72, No. 4 (1972), p. 358.

Charles W. Trigg, Infinite sequences of palindromic triangular numbers, The Fibonacci Quarterly, Vol. 12, No. 2 (1974), pp. 209-212.

Maciej Ulas, On certain diophantine equations related to triangular and tetrahedral numbers, arXiv:0811.2477 [math.NT], 2008.

Example

10 is a term since 10 = A000217(4) is a triangular number and also a palindromic number in base 3: 10 = 101_3.
28 is a term since 28 = A000217(7) is a triangular number and also a palindromic number in base 3: 36 = 1001_3.

Mathematica

t[n_] := n*(n + 1)/2; Select[t /@ Range[0, 3*10^5], PalindromeQ[IntegerDigits[#, 3]] &]

Crossrefs

Intersection of A000217 and A014190.

The ternary version of A003098.

Cf. A003462, A350987, A350991, A350992, A350993.

Sequence in context: A076712 A116973 A352180 * A264579 A003665 A332432

Adjacent sequences: A350987 A350988 A350989 * A350991 A350992 A350993

Keyword

nonn,base

Author

Amiram Eldar, Jan 28 2022

Status

approved