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A372547
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Palindromic Zumkeller numbers in base 10.
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1
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6, 66, 88, 222, 252, 272, 282, 414, 444, 464, 474, 606, 616, 636, 666, 696, 828, 858, 868, 888, 2002, 2112, 2442, 2552, 2772, 2992, 4004, 4224, 4554, 4664, 4884, 5775, 6006, 6336, 6666, 6776, 6996, 8008, 8118, 8228, 8448, 8778, 8888, 20202, 20502, 20802, 21012, 21112, 21312
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OFFSET
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1,1
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COMMENTS
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1x1, where x stands for zero or more zeros, is never divisible by 2 and 3. Since 2*3*1x1 is always a Zumkeller number, it follows that there are infinitely many terms.
Based on the conjecture that there are infinitely many repunit primes, one may conjecture there are infinitely many repdigit terms, since 2*3*y (where y is a repunit prime) is a repdigit palindromic Zumkeller number.
Note that A098775 is not a subsequence: not every abundant number is a Zumkeller number. E.g., 22122 is in A098775 but is not here. - Amiram Eldar, May 05 2024
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LINKS
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MATHEMATICA
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zn=Cases[Import["https://oeis.org/A083207/b083207.txt", "Table"], {_, _}][[All, 2]]; Select[zn, PalindromeQ[#]&]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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