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.
[NthPrime(n): n in [1..5000] | (Intseq(NthPrime(n), 2) eq Reverse(Intseq(NthPrime(n), 2)))]; // Vincenzo Librandi, Feb 24 2018
lst = {}; Do[ If[ PrimeQ@n, t = IntegerDigits[n, 2]; If[ FromDigits@t == FromDigits@ Reverse@ t, AppendTo[lst, n]]], {n, 3, 50000, 2}]; lst (* syntax corrected by Robert G. Wilson v, Aug 10 2009 *)
pal2Q[n_] := Reverse[x = IntegerDigits[n, 2]] == x; Select[Prime[Range[2800]], pal2Q[#] &] (* Jayanta Basu, Jun 23 2013 *)
genPal[n_Integer, base_Integer: 10] := Block[{id = IntegerDigits[n, base], insert = Join[{{}}, {# - 1} & /@ Range[base]]}, FromDigits[#, base] & /@ (Join[id, #, Reverse@id] & /@ insert)]; k = 0; lst = {}; While[k < 100, AppendTo[lst, Select[ genPal[k, 2], PrimeQ]]; lst = Flatten@ lst; k++]; lst (* Robert G. Wilson v, Feb 23 2018 *)
is(n)=isprime(n)&&Vecrev(n=binary(n))==n \\ M. F. Hasler, Feb 23 2018
from sympy import isprime def ok(n): return isprime(n) and (b:=bin(n)[2:]) == b[::-1] print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Apr 20 2024
Fibonacci base columns are ...,8,5,3,2,1 with column entries 0 or 1 and no two consecutive ones (the Zeckendorf representation) so that each n has a unique representation. 12 is in the sequence because 12 = 8 + 3 + 1 = 10101 base Fib; 14 = 13 + 1 = 100001 base Fib.
zeck[n_Integer] := Block[{k = Ceiling[ Log[ GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[ fr, 1]; t = t - Fibonacci[k], AppendTo[fr, 0]]; k-- ]; FromDigits[fr]]; a = {}; Do[z = zeck[n]; If[ FromDigits[ Reverse[ IntegerDigits[z]]] == z, AppendTo[a, n]], {n, 1123}]; a (* Robert G. Wilson v, May 29 2004 *)
mirror[dig_, s_] := Join[dig, s, Reverse[dig]]; select[v_, mid_] := Select[v, Length[#] == 0 || Last[#] != mid &]; fib[dig_] := Plus @@ (dig * Fibonacci[Range[2, Length[dig] + 1]]); pals = Rest[IntegerDigits /@ FromDigits /@ Select[Tuples[{0, 1}, 7], SequenceCount[#, {1, 1}] == 0 &]]; Union@Join[{0, 1}, fib /@ Join[mirror[#, {}] & /@ (select[pals, 1]), mirror[#, {1}] & /@ (select[pals, 1]), mirror[#, {0}] & /@ pals]] (* Amiram Eldar, Jan 11 2020 *)
from sympy import fibonacci
def a(n):
k=0
x=0
while n>0:
k=0
while fibonacci(k)<=n: k+=1
x+=10**(k - 3)
n-=fibonacci(k - 1)
return x
def ok(n):
x=str(a(n))
return x==x[::-1]
print([n for n in range(1101) if ok(n)]) # Indranil Ghosh, Jun 07 2017
a(1) = a(2) = 0, as there are no primes in ranges [1,2[ and [2,3[. a(3)=1 as in [3,5[ there is prime 3 with Fibonacci-representation 100, which is just a one fibit-flip away from being a palindrome (i.e. A095734(3)=1). a(4)=3, as in [5,8[ there are primes 5 and 7, whose Fibonacci-representations are 1000 and 1010 respectively and the other needs one bit-flip and the other two to become palindromes and 1 + 2 = 3. a(5)=1, as in [8,13[ there is only one prime 11, with Zeckendorf-representation 10100, which needs to have just its least significant fibit flipped from 0 to 1 to become palindrome.
The first such prime is 127 = F(2)+F(4)+F(9)+F(11) (which thus has a symmetric Zeckendorf-expansion as 1010000101).
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