A350993 Triangular numbers that are palindromes in base 9.

0, 1, 3, 6, 10, 91, 136, 300, 528, 820, 4560, 7381, 11476, 20910, 42486, 66430, 552826, 581581, 597871, 1664400, 2001000, 3420420, 3444000, 5070520, 5380840, 48427561, 75995956, 132494781, 134553810, 137158203, 159213090, 290585778, 434520460, 435848050, 669615310

Offset

1,3

Comments

This sequence is infinite since A000217((9^k-1)/2) is a term for all k >= 0 (Wishard, 1931).

Also, A000217((3 + 5*9^k)/2) is a term for all k>=0 (Trigg, 1984).

References

Charles W. Trigg, Mathematical Quickies, McGraw Hill Book Co., 1967, Q112, p. 127.

Links

Amiram Eldar, Table of n, a(n) for n = 1..123

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

Charles W. Trigg, Probelm 281, The College Mathematics Journal, Vol. 15, No. 4 (1984), p. 346; Palindromic Triangular Numbers in Base Nine, Solution to Problem 281, by Michael Vowe, ibid., Vol. 17, No. 2 (1986), pp. 188-189.

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

G. W. Wishard, Problem 3480, The American Mathematical Monthly, Vol. 38, No. 3 (1931), p. 170; Solution to Problem 3480, by Helen A. Merrill, ibid., Vol. 39, No. 3 (1932), p. 179.

Example

10 is a term since 10 = A000217(4) is a triangular number and also a palindromic number in base 9: 10 = 11_9.
91 is a term since 91 = A000217(13) is a triangular number and also a palindromic number in base 9: 91 = 111_9.

Mathematica

t[n_] := n*(n + 1)/2; Select[t /@ Range[0, 3*10^5], PalindromeQ[IntegerDigits[#, 9]] &]

Crossrefs

Intersection of A000217 and A029955.

The nonary version of A003098.

Cf. A191681, A350987, A350990, A350991, A350992.

Sequence in context: A338767 A351131 A061380 * A308849 A354000 A368173

Adjacent sequences: A350990 A350991 A350992 * A350994 A350995 A350996

Keyword

nonn,base

Author

Amiram Eldar, Jan 28 2022

Status

approved