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A350993
Triangular numbers that are palindromes in base 9.
5
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
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.
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.
Sequence in context: A338767 A351131 A061380 * A308849 A354000 A368173
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jan 28 2022
STATUS
approved