A046807 Palindromes in factorial base.

0, 1, 3, 7, 9, 11, 25, 33, 41, 121, 127, 133, 139, 147, 153, 159, 165, 173, 179, 185, 191, 721, 751, 781, 811, 843, 873, 903, 933, 965, 995, 1025, 1055, 5041, 5065, 5089, 5113, 5137, 5167, 5191, 5215, 5239, 5263, 5293, 5317, 5341, 5365, 5389, 5419, 5443, 5467

Offset: 1

Author

Erich Friedman

Keywords

• base
• nonn

Comments

Equivalently numbers n such that row n of A108731 is symmetric. - Rémy Sigrist, Mar 20 2018

Examples

			41 = 1 4! + 2 3! + 2 2! + 1 1!.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms n = 1..1000 from _Rémy Sigrist_)
• Index entries for sequences related to factorial base representation
• Index entries for sequences related to palindromes

Crossrefs

Cf. A108731.

Programs

PARI

is(n) = my (d=[]); for (r=2, oo, if (n==0, return (Vecrev(d)==d), d=concat(n%r, d); n\=r)) \\ Rémy Sigrist, Mar 19 2018

Python

from math import factorial
from itertools import count, islice, product
def palgen(): # generator of palindromic representations in the factorial base
    yield from [(0,), (1,)]
    for d in count(2):
        pp = []
        for i in range(2, (d+1)//2+1):
            pp.append(range(0, i+1))
        for t in product(*pp):
            right = t
            left = right[:-1][::-1] if d&1 else right[::-1]
            yield (1, ) + right + left + (1, )
def A046807_gen(): # generator of terms
    yield from (sum(dj*factorial(j) for j, dj in enumerate(t[::-1], 1)) for t in palgen())
print(list(islice(A046807_gen(), 51))) # Michael S. Branicky, Mar 09 2025

Extensions

More terms from Floor van Lamoen, Oct 31 2001

Data corrected and initial 0 added by Rémy Sigrist, Mar 19 2018