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.
11 is the sixth Lucas number and it is also palindromic in base 10.
Select[LucasL[Range[0,200]],PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 26 2018 *)
a(1) = 0 (as Fibonacci(0) = 0 is the smallest Fibonacci number). a(2) = 10 (Fibonacci(10) = 55 is the only 2-digit Fibonacci number that is palindromic, and almost certainly the only multidigit palindromic Fibonacci number; see A045504). a(3) = 317 because Fibonacci(317) (a 66-digit number) is the smallest Fibonacci number whose first 3 digits (793) are the reverse of its last 3 digits (397). The table below lists the first 8 terms and the corresponding Fibonacci numbers (abbreviated, for n > 2): . n a(n) Fibonacci(a(n)) - --------- ------------------- 1 0 0 2 10 55 3 317 793...397 4 1235 5626...6265 5 28898 94480...08449 6 120742 172255...552271 7 1411753 3789665...5669873 8 201095722 11367389...98376311
/* See links. */
a := proc(n) if n < 4 then n else simplify(hypergeom([-n/3, (1-n)/3, (-1-n)/3], [-n/2, (-1-n)/2], -27/4)); convert(%, base, 10); ListTools:-Reverse(%); if %% = % then add(%[k]*10^(k-1), k=1..nops(%)) else NULL fi fi end: seq(a(n), n=1..200); # Peter Luschny, Nov 07 2017
A000045(6) = 8. In base 2 this is 1000, not a palindrome, but in base 3 it is 22, a palindrome. Thus a(6) = 3.
f:= proc(x) local b,L;
for b from 2 do
L:= convert(x,base,b);
if L = ListTools:-Reverse(L) then return b fi
od
end proc:
map(f, [seq(combinat:-fibonacci(n), n=1..70)]);
A372754[n_] := Block[{b = 1}, While[!PalindromeQ[IntegerDigits[#, ++b]]] & [Fibonacci[n]]; b]; Array[A372754, 70] (* Paolo Xausa, May 18 2024 *)
from itertools import count from sympy import fibonacci from sympy.ntheory.factor_ import digits def A372754(n): return next(b for b in count(2) if (s := digits(fibonacci(n),b)[1:])[:(t:=len(s)+1>>1)]==s[:-t-1:-1]) # Chai Wah Wu, May 13 2024
t = {}; Do[b = IntegerDigits[Fibonacci[n], 2]; If[b == Reverse[b], AppendTo[t, n]], {n, 0, 1000}]; t (* T. D. Noe, Dec 14 2013 *)
Select[Range[0,10],PalindromeQ[IntegerDigits[Fibonacci[#],2]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 04 2019 *)
a = c = 0; b = 1; lst = {0}; While[a < 10^7, d = a + b + c; If[ Reverse[idn = IntegerDigits[d]] == idn, AppendTo[lst, d]]; a = b; b = c; c = d]; lst (* Robert G. Wilson v, Nov 09 2017 *)
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