A307348 -id:A307348 - cp's OEIS frontend

A307367 Number of palindromic triangular numbers with exactly n digits.

4, 2, 3, 3, 2, 2, 6, 2, 1, 4, 7, 0, 4, 4, 12, 5, 6, 2, 3, 2, 6, 3, 6, 2, 2, 4, 3, 2, 5, 0, 3, 2, 1, 4, 3, 1, 10, 1, 4, 0, 3, 2, 2, 1, 1

Offset: 1

Robert Price, May 01 2019

Number of terms in A003098 with exactly n digits.

Differs from A054263 only at a(1), assuming 0 has 1 digits. - R. J. Mathar, May 06 2019

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

Cf. A000217, A003098, A008509, A034822, A263618, A307348.

A003098 = Select[PolygonalNumber[3, Range[0, 10^6]], PalindromeQ];
  (* Set Range to level of desired running time. \ *)
Table[Length[ Select[A003098, IntegerLength[#] == n || (n == 1 && # == 0) &]], {n, 12}]
  (* Set Range to encompass length of last value in A003098. *)

A307850 Number of palindromic triangular numbers of length n whose index is also palindromic.

Original entry on oeis.org

4, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Robert Price, May 01 2019

			There is only one palindromic triangular number of length 2 whose index is also palindromic. 11->66. Thus, a(2)=1.

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

Cf. A000217, A003098, A008509, A307348, A307367.

A003098 = Select[PolygonalNumber[3, Range[0, 10^6]], PalindromeQ]
  (* Set Range to level of desired running time. *)
A008509 = Select[Range[0, 10^6], PalindromeQ[PolygonalNumber[3, #]] &]
  (* Set Range to level of desired running time. *)
Table[Length[ Select[A008509[[Table[ Select[Range[35], IntegerLength[A003098[[#]]] == n || (n == 1 && A003098[[#]] == 0) &], {35}][[n]]]], PalindromeQ[#] &]], {n, 11}]
  (* Set the first two Ranges to encompass the length of A003098 and  the last Range to encompass the length of the last value in A003098. *)

cp's OEIS Frontend

A307367 Number of palindromic triangular numbers with exactly n digits.

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