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.

A282585 Number of ways to write n as an ordered sum of 3 squarefree palindromes (A071251).

Original entry on oeis.org

0, 0, 0, 1, 3, 6, 7, 9, 12, 19, 21, 21, 18, 24, 27, 28, 18, 18, 19, 24, 15, 10, 6, 12, 12, 12, 9, 9, 12, 15, 18, 12, 9, 7, 15, 15, 15, 9, 12, 15, 18, 18, 12, 9, 9, 18, 15, 12, 0, 9, 9, 9, 0, 0, 0, 6, 6, 9, 12, 9, 12, 15, 18, 18, 12, 9, 13, 18, 18, 18, 9, 15, 18, 21, 18, 12, 9, 15, 21, 21, 21, 9, 18, 21, 24, 18
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 19 2017

Keywords

Comments

Every number can be written as the sum of 3 palindromes (see A261132 and A261422).
Conjecture: a(n) > 0 for any sufficiently large n.
Additional conjecture: every number > 3 can be written as the sum of 4 squarefree palindromes.

Examples

			a(22) = 6 because we have [11, 6, 5], [11, 5, 6] [6, 11, 5], [6, 5, 11], [5, 11, 6] and [5, 6, 11].

Links

Crossrefs

Cf. A002113, A005117, A035137, A071251, A091580, A091581, A260254, A261131, A261132, A261422, A280210, A282584.

Programs

  • Mathematica
    nmax = 85; CoefficientList[Series[Sum[Boole[SquareFreeQ[k] && PalindromeQ[k]] x^k, {k, 1, nmax}]^3, {x, 0, nmax}], x]

Formula

G.f.: (Sum_{k>=1} x^A071251(k))^3.

A286970 Number of compositions (ordered partitions) of n into decimal palindromic primes (A002385).

Original entry on oeis.org

1, 0, 1, 1, 1, 3, 2, 6, 6, 10, 16, 20, 35, 45, 72, 103, 150, 228, 324, 491, 710, 1053, 1552, 2272, 3369, 4930, 7288, 10711, 15771, 23244, 34175, 50382, 74113, 109168, 160722, 236596, 348446, 512894, 755303, 1111946, 1637205, 2410592, 3549023, 5225659, 7693623, 11327912
Offset: 0

Views

Author

Ilya Gutkovskiy, May 17 2017

Keywords

Examples

			a(7) = 6 because we have [7], [5, 2], [3, 2, 2], [2, 5], [2, 3, 2] and [2, 2, 3].

Links

Crossrefs

Cf. A002385, A023360, A282584.

Programs

  • Mathematica
    nmax = 45; CoefficientList[Series[1/(1 - Sum[Boole[PalindromeQ[k] && PrimeQ[k]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^A002385(k)).

A338847 Number of compositions (ordered partitions) of n into distinct decimal palindromes.

Original entry on oeis.org

1, 1, 1, 3, 3, 5, 11, 13, 19, 27, 56, 63, 98, 122, 180, 324, 376, 538, 710, 962, 1130, 2202, 2341, 3410, 4226, 5276, 6692, 8324, 13940, 15476, 21692, 22394, 32952, 33555, 43418, 47738, 93002, 92282, 101666, 136346, 140810, 176186, 176336, 212448
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 11 2020

Keywords

Links

Crossrefs

Cf. A002113, A091580, A091581, A282584.
Showing 1-3 of 3 results.

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

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