A307802 -id:A307802 - cp's OEIS frontend

A307807 Number of palindromic nonagonal numbers with exactly n digits.

3, 0, 3, 1, 2, 0, 2, 2, 5, 2, 1, 2, 0, 0, 0, 0, 1, 2, 3, 0, 1, 1

Offset: 1

Robert Price, Apr 29 2019

Number of terms in A082723 with exactly n digits.

			There are only three 3 digit nonagonal numbers that are palindromic, 111, 474 and 969.  Thus, a(3)=3.

G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy] See page 95.

Cf. A001106, A055560, A082722, A082733, A307801, A307802.

A082723 = {0, 1, 9, 111, 474, 969, 6666, 18981, 67276, 4411144, 6964696, 15444451, 57966975, 448707844, 460595064, 579696975, 931929139, 994040499, 1227667221, 9698998969, 61556965516, 664248842466, 699030030996, 99451743334715499, 428987160061789824, 950178723327871059, 1757445628265447571, 4404972454542794044, 9433971680861793349, 499583536595635385994, 1637992008558002997361, 19874891310701319847891}; Table[Length[Select[A082723, IntegerLength[#] == n || (n == 1 && # == 0) &]], {n, 22}]

A307808 Number of palindromic nonagonal numbers of length n whose index is also palindromic.

Original entry on oeis.org

3, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Robert Price, Apr 29 2019

Is there a nonzero term beyond a(4)?

			There is only one palindromic nonagonal number of length 4 whose index is also palindromic, 44->6666. Thus, a(4)=1.

Patrick De Geest, Palindromic Squares in bases 2 to 17
Eric Weisstein's World of Mathematics, Palindromic Number

Cf. A001106, A055560, A082722, A082733, A307801, A307802.

A082723 = {0, 1, 9, 111, 474, 969, 6666, 18981, 67276, 4411144, 6964696, 15444451, 57966975, 448707844, 460595064, 579696975, 931929139, 994040499, 1227667221, 9698998969, 61556965516, 664248842466, 699030030996, 99451743334715499, 428987160061789824, 950178723327871059, 1757445628265447571, 4404972454542794044, 9433971680861793349, 499583536595635385994, 1637992008558002997361, 19874891310701319847891};
A055560 = {0, 1, 2, 6, 12, 17, 44, 74, 139, 1123, 1411, 2101, 4070, 11323, 11472, 12870, 16318, 16853, 18729, 52642, 132619, 435644, 446904, 168566853, 350096787, 521037077, 708609429, 1121857192, 1641773578, 11947307367, 21633254881, 75356090494};
Table[Length[Select[A055560[[Table[Select[Range[22], IntegerLength[A082723[[#]]] ==  n || (n == 1 && A082723[[#]] == 0) &], {n, 22}][[n]]]], PalindromeQ[#] &]], {n, 22}]

cp's OEIS Frontend

A307807 Number of palindromic nonagonal numbers with exactly n digits.

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