A372547 Palindromic Zumkeller numbers in base 10.

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

Offset

1,1

Comments

Intersection of A002113 and A083207.

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..435 (terms below 10^6; terms 1..263 from R. J. Mathar)

Mathematica

zn=Cases[Import["https://oeis.org/A083207/b083207.txt", "Table"], {_, _}][[All, 2]]; Select[zn, PalindromeQ[#]&]

Crossrefs

Cf. A002113, A083207, A098775.

Sequence in context: A137121 A110222 A119230 * A122780 A153514 A119144

Adjacent sequences: A372544 A372545 A372546 * A372548 A372549 A372550

Keyword

nonn,base

Author

Ivan N. Ianakiev, May 05 2024

Status

approved