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A046807 Palindromes in factorial base.

%I A046807 #21 Mar 10 2025 11:11:32
%S A046807 0,1,3,7,9,11,25,33,41,121,127,133,139,147,153,159,165,173,179,185,
%T A046807 191,721,751,781,811,843,873,903,933,965,995,1025,1055,5041,5065,5089,
%U A046807 5113,5137,5167,5191,5215,5239,5263,5293,5317,5341,5365,5389,5419,5443,5467
%N A046807 Palindromes in factorial base.
%C A046807 Equivalently numbers n such that row n of A108731 is symmetric. - _Rémy Sigrist_, Mar 20 2018
%H A046807 Michael S. Branicky, <a href="/A046807/b046807.txt">Table of n, a(n) for n = 1..10000</a> (terms n = 1..1000 from _Rémy Sigrist_)
%H A046807 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%H A046807 <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>
%e A046807 41 = 1 4! + 2 3! + 2 2! + 1 1!.
%o A046807 (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
%o A046807 (Python)
%o A046807 from math import factorial
%o A046807 from itertools import count, islice, product
%o A046807 def palgen(): # generator of palindromic representations in the factorial base
%o A046807     yield from [(0,), (1,)]
%o A046807     for d in count(2):
%o A046807         pp = []
%o A046807         for i in range(2, (d+1)//2+1):
%o A046807             pp.append(range(0, i+1))
%o A046807         for t in product(*pp):
%o A046807             right = t
%o A046807             left = right[:-1][::-1] if d&1 else right[::-1]
%o A046807             yield (1, ) + right + left + (1, )
%o A046807 def A046807_gen(): # generator of terms
%o A046807     yield from (sum(dj*factorial(j) for j, dj in enumerate(t[::-1], 1)) for t in palgen())
%o A046807 print(list(islice(A046807_gen(), 51))) # _Michael S. Branicky_, Mar 09 2025
%Y A046807 Cf. A108731.
%K A046807 base,nonn
%O A046807 1,3
%A A046807 _Erich Friedman_
%E A046807 More terms from _Floor van Lamoen_, Oct 31 2001
%E A046807 Data corrected and initial 0 added by _Rémy Sigrist_, Mar 19 2018