cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A307830 Numbers k for which there exist no palindromic decagonal numbers (also known as 10-gonals) of length k.

Original entry on oeis.org

2, 4, 6, 7, 9, 11, 16, 18, 19
Offset: 1

Views

Author

Robert Price, Apr 30 2019

Keywords

Links

Crossrefs

Cf. A001107, A082722, A307827, A307829.

Programs

  • Mathematica
    A307827 = {0, 1, 232, 27972, 76867, 25555552, 7154664517, 158229922851, 2028787878202, 2040061600402, 2733623263372, 52667666676625, 675972505279576, 28519896169891582, 73542836563824537, 74529570707592547, 25552469511596425552, 27835145788754153872, 62740719088091704726, 67047523077032574076, 77979812588521897977, 107838025535520838701};
a[n_] := Length[Select[A307827, IntegerLength[#] == n || (n == 1 && # == 0) &]];
Select[Range[20], a[#] == 0 &]

A307831 Number of palindromic decagonal (10-gonal) numbers with exactly n digits.

Original entry on oeis.org

2, 0, 1, 0, 2, 0, 0, 1, 0, 1, 0, 1, 3, 1, 1, 0, 3, 0, 0, 5
Offset: 1

Views

Author

Robert Price, Apr 30 2019

Keywords

Comments

Number of terms in A307827 with exactly n digits.

Examples

			There are only two 5 digit decagonal numbers that are palindromic, 27972 and 76867. Thus, a(5)=2.

Links

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

Crossrefs

Cf. A001107, A307827, A307829, A307830, A307807.

Programs

  • Mathematica
    A307827 = {0, 1, 232, 27972, 76867, 25555552, 7154664517, 158229922851, 2028787878202, 2040061600402, 2733623263372, 52667666676625, 675972505279576, 28519896169891582, 73542836563824537, 74529570707592547, 25552469511596425552, 27835145788754153872, 62740719088091704726, 67047523077032574076, 77979812588521897977, 107838025535520838701};
Table[Length[ Select[A307827, IntegerLength[#] == n || (n == 1 && # == 0) &]], {n, 20}]

A307832 Number of palindromic decagonal (10-gonal) numbers of length n whose index is also palindromic.

Original entry on oeis.org

2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Robert Price, Apr 30 2019

Keywords

Comments

Is there a nonzero term beyond a(12)?

Examples

			There is only one palindromic decagonal number of length 3 whose index is also palindromic, 8->232. Thus, a(3)=1.

Links

Crossrefs

Cf. A001107, A307827, A307829, A307830, A307831, A307808.

Programs

  • Mathematica
    A307827 = {0, 1, 232, 27972, 76867, 25555552, 7154664517, 158229922851, 2028787878202, 2040061600402, 2733623263372, 52667666676625, 675972505279576, 28519896169891582, 73542836563824537, 74529570707592547, 25552469511596425552, 27835145788754153872, 62740719088091704726, 67047523077032574076, 77979812588521897977, 107838025535520838701};
A307829 = {0, 1, 8, 84, 139, 2528, 42293, 198891, 712178, 714154, 826684, 3628625, 12999736, 84439174, 135593913, 136500523, 2527472528, 2637951184, 3960451966, 4094127596, 4415308953, 5192254461};
Table[Length[ Select[A307829[[Table[ Select[Range[20], IntegerLength[A307827[[#]]] == n || (n == 1 && A307827[[#]] == 0) &], {n, 20}][[n]]]], PalindromeQ[#] &]], {n, 20}]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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