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A350988
Numbers k such that the k-th triangular number is a binary palindrome.
3
0, 1, 2, 5, 6, 9, 17, 21, 25, 33, 42, 65, 90, 129, 170, 257, 341, 357, 450, 513, 693, 893, 1025, 1365, 1397, 1445, 1617, 1670, 1750, 2049, 2730, 4097, 5418, 5985, 8193, 10397, 10922, 16385, 17313, 21717, 21845, 31749, 32769, 40637, 43605, 51537, 63482, 65537, 76217
OFFSET
1,3
COMMENTS
This sequence is infinite since 2^k+1 is a term for all k>1 (Trigg, 1974).
LINKS
Charles W. Trigg, Infinite sequences of palindromic triangular numbers, The Fibonacci Quarterly, Vol. 12, No. 2 (1974), pp. 209-212.
FORMULA
A000217(a(n)) = A350987(n).
EXAMPLE
2 is a term since A000217(2) = 2*(2+1)/2 = 3 = 11_2 is a triangular number and also a binary palindromic number.
5 is a term since A000217(5) = 5*(5+1)/2 = 15 = 1111_2 is a triangular number and also a binary palindromic number.
MATHEMATICA
Select[Range[0, 10^5], PalindromeQ[IntegerDigits[#*(# + 1)/2, 2]] &]
PROG
(PARI) isok(k) = my(b=binary(k*(k+1)/2)); b == Vecrev(b); \\ Michel Marcus, Jan 28 2022
(Python)
def ok(n): b = bin(n*(n+1)//2)[2:]; return b == b[::-1]
print([k for k in range(80000) if ok(k)]) # Michael S. Branicky, Jan 28 2022
CROSSREFS
The binary version of A008509.
A000051 \ {3} is a subsequence.
Sequence in context: A301791 A051677 A122965 * A226810 A054463 A295741
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jan 28 2022
STATUS
approved