A002113 -id:A002113 - cp's OEIS frontend

A029953 Palindromic in base 6.

0, 1, 2, 3, 4, 5, 7, 14, 21, 28, 35, 37, 43, 49, 55, 61, 67, 74, 80, 86, 92, 98, 104, 111, 117, 123, 129, 135, 141, 148, 154, 160, 166, 172, 178, 185, 191, 197, 203, 209, 215, 217, 259, 301, 343, 385, 427, 434, 476, 518, 560, 602, 644, 651, 693, 735, 777, 819

Offset: 1

Patrick De Geest

Cilleruelo, Luca, & Baxter prove that this sequence is an additive basis of order (exactly) 3. - Charles R Greathouse IV, May 03 2020

T. D. Noe, Table of n, a(n) for n = 1..10000
Javier Cilleruelo, Florian Luca and Lewis Baxter, Every positive integer is a sum of three palindromes, Mathematics of Computation, Vol. 87, No. 314 (2018), pp. 3023-3055, arXiv preprint, arXiv:1602.06208 [math.NT], 2017.
Patrick De Geest, Palindromic numbers beyond base 10.
Phakhinkon Phunphayap and Prapanpong Pongsriiam, Estimates for the Reciprocal Sum of b-adic Palindromes, 2019.
Index entries for sequences that are an additive basis, order 3.

Palindromes in bases 2 through 10: A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955, A002113.

[n: n in [0..900] | Intseq(n, 6) eq Reverse(Intseq(n, 6))]; // Vincenzo Librandi, Sep 09 2015

f[n_,b_] := Module[{i=IntegerDigits[n,b]}, i==Reverse[i]]; lst={}; Do[If[f[n,6], AppendTo[lst,n]], {n,1000}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)

ispal(n,b=6)=my(d=digits(n,b)); d==Vecrev(d) \\ Charles R Greathouse IV, May 03 2020

from gmpy2 import digits
from sympy import integer_log
def A029953(n):
    if n == 1: return 0
    y = 6*(x:=6**integer_log(n>>1,6)[0])
    return int((c:=n-x)*x+int(digits(c,6)[-2::-1]or'0',6) if nChai Wah Wu, Jun 14 2024

Sum_{n>=2} 1/a(n) = 3.03303318... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020

A062687 Numbers all of whose divisors are palindromic.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 121, 131, 151, 181, 191, 202, 242, 262, 303, 313, 353, 363, 373, 383, 393, 404, 484, 505, 606, 626, 707, 727, 757, 787, 797, 808, 909, 919, 929, 939, 1111, 1331, 1441, 1661, 1991, 2222, 2662

Offset: 1

Erich Friedman, Jul 04 2001

			The divisors of 44 are 1, 2, 4, 11, 22 and 44, which are all palindromes, so 44 is in the sequence.
808 has divisors are 1, 2, 4, 8, 101, 202, 404, 808, so 808 is in the sequence.
818 is palindromic, but since it's 2 * 409, it's not in the sequence.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..221 from Indranil Ghosh)

Cf. A087991, A084325, A002385 (subset).

Subsequence of A002113.

isA062687 := proc(n)
    for d in numtheory[divisors](n) do
        if not isA002113(d) then
            return false;
        end if;
    end do;
    true ;
end proc: # R. J. Mathar, Sep 09 2015

palQ[n_] := Module[{idn = IntegerDigits[n]}, idn == Reverse[idn]]; Select[Range[2750], And@@palQ/@Divisors[#] &] (* Harvey P. Dale, Feb 27 2012 *)

isok(n) = {d = divisors(n); rd = vector(#d, i, subst(Polrev(digits(d[i])), x, 10)); (d == rd);} \\ Michel Marcus, Oct 10 2014

A055483 a(n) is the GCD of n and the reverse of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 3, 1, 1, 3, 1, 1, 9, 1, 2, 3, 22, 1, 6, 1, 2, 9, 2, 1, 3, 1, 1, 33, 1, 1, 9, 1, 1, 3, 4, 1, 6, 1, 44, 9, 2, 1, 12, 1, 5, 3, 1, 1, 9, 55, 1, 3, 1, 1, 6, 1, 2, 9, 2, 1, 66, 1, 2, 3, 7, 1, 9, 1, 1, 3, 1, 77, 3, 1, 8, 9, 2, 1, 12, 1, 2, 3, 88, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 99, 1, 101, 3, 1, 1, 3, 1, 1, 9, 1, 11, 111

Offset: 1

Erich Friedman, Jun 27 2000

a(A226778(n)) = 1; a(A071249(n)) > 1. - Reinhard Zumkeller, Jun 18 2013

a(n) = n iff n >= 1 is a palindrome (n is in A002113). - Felix Fröhlich, Oct 28 2014

			a(12) = 3 since gcd(12, 21) = 3.
a(13) = 1 since 13 and 31 are coprime.
a(101) = gcd(101, 101) = 101.

Indranil Ghosh, Table of n, a(n) for n = 1..50000 (first 1000 terms from T. D. Noe)

Different from A069652, first differs at a(101), since gcd(101, 110) = 1.

Cf. A002113, A004086, A071249, A226778.

a055483 n = gcd n $ a004086 n  -- Reinhard Zumkeller, Jun 18 2013

[Gcd(n, Seqint(Reverse(Intseq(n)))): n in [1..100]]; // Vincenzo Librandi, Oct 29 2014

gcn[n_] := GCD[n, IntegerReverse[n]]; Array[gcn, 120] (* Harvey P. Dale, Jan 23 2012 *)

a004086(n)=eval(concat(Vecrev(Str(n))))
a(n)=gcd(n, a004086(n)) \\ Felix Fröhlich, Oct 28 2014

from math import gcd
def a(n): return gcd(n, int(str(n)[::-1]))
print([a(n) for n in range(1, 112)]) # Michael S. Branicky, Aug 31 2021

def reverseDigits(n: Int): Int = Integer.parseInt(n.toString.reverse)
def euclGCD(a: Int, b: Int): Int = b match { case 0 => a; case n => Math.abs(euclGCD(b, a % b)) }
(1 to 120).map(n => euclGCD(n, reverseDigits(n))) // Alonso del Arte, Aug 31 2021

a(n) = gcd(n, A004086(n)). - Felix Fröhlich, Oct 28 2014

3 | a(n) if 3 | n and 9 | a(n) if 9 | n. - Alonso del Arte, Aug 31 2021

Edited by Robert G. Wilson v, Apr 10 2002

A035137 Numbers that are not the sum of 2 palindromes (where 0 is considered a palindrome).

Original entry on oeis.org

21, 32, 43, 54, 65, 76, 87, 98, 201, 1031, 1041, 1042, 1051, 1052, 1053, 1061, 1062, 1063, 1064, 1071, 1072, 1073, 1074, 1075, 1081, 1082, 1083, 1084, 1085, 1086, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1099, 1101, 1103, 1104, 1105, 1106, 1107, 1108

Offset: 1

Patrick De Geest, Nov 15 1998

Apparently, every positive number is equal to the sum of at most 3 positive palindromes. - Giovanni Resta, May 12 2013
A260254(a(n)) = 0. - Reinhard Zumkeller, Jul 21 2015
A261675(a(n)) >= 3 (and, conjecturally, = 3). - N. J. A. Sloane, Sep 03 2015
This sequence is infinite. Proof: It is easy to see that 200...01 (with any number of zeros) cannot be the sum of two palindromes. - N. J. A. Sloane, Sep 03 2015
The conjecture that every number is the sum of 3 palindromes fails iff there is a term a(n) such that for all palindromes P < a(n), the difference a(n) - P is also a term of this sequence. - M. F. Hasler, Sep 08 2015
Cilleruelo and Luca (see links) have proved the conjecture that every positive integer is the sum of at most three palindromes (in bases >= 5), and also that the density of those that require three is positive. - Christopher E. Thompson, Apr 14 2016

David W. Wilson, Table of n, a(n) for n = 1..10000
Javier Cilleruelo and Florian Luca, Every positive integer is a sum of three palindromes, arXiv:1602.06208 [math.NT], 2016.
P. De Geest, World!Of Numbers
Hugo Pfoertner, Plot of first 10^6 terms
Eric Weisstein's World of Mathematics, Palindromic Number

Cf. A014091, A014092, A104444.
Cf. A260254, A260255 (complement), A002113, A261906, A261907.
Cf. A319477 (disallowing zero).

a035137 n = a035137_list !! (n-1)
a035137_list = filter ((== 0) . a260254) [0..]
-- Reinhard Zumkeller, Jul 21 2015

N:= 4: # to get all terms with <= N digits
revdigs:= proc(n) local L,j,nL;
  L:= convert(n,base,10); nL:= nops(L);
  add(L[j]*10^(nL-j),j=1..nL);
end proc;
palis:= $0..9:
for d from 2 to N do
  if d::even then
    palis:= palis, seq(x*10^(d/2)+revdigs(x),x=10^(d/2-1)..10^(d/2)-1)
  else
    palis:= palis, seq(seq(x*10^((d+1)/2)+y*10^((d-1)/2)+revdigs(x),y=0..9),x=10^((d-3)/2)..10^((d-1)/2)-1);
  fi
od:
palis:= [palis]:
A:= Array(0..10^N-1):
A[palis]:= 1:
B:= SignalProcessing:-Convolution(A,A):
select(t -> B[t+1] < 0.5, [$1..10^N-1]); # Robert Israel, Jun 22 2015

palQ[n_]:=FromDigits[Reverse[IntegerDigits[n]]]==n; nn=1108; t={}; Do[i=c=0; While[i<=n && c!=1,If[palQ[i] && palQ[n-i], AppendTo[t,n]; c=1]; i++],{n,nn}]; Complement[Range[nn],t] (* Jayanta Basu, May 12 2013 *)

is_A035137(n)={my(k=0);!until(n<2*k=nxt(k),is_A002113(n-k)&&return)} \\ Uses function nxt() given in A002113. Not very efficient for large n, better start with k=n-A261423(n). Maybe also better use A261423 rather than nxt(). - M. F. Hasler, Jul 21 2015

A033620 Numbers all of whose prime factors are palindromes.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 98, 99, 100, 101, 105, 108, 110, 112, 120, 121, 125, 126, 128, 131

Offset: 1

N. J. A. Sloane, May 17 1998

Multiplicative closure of A002385; A051038 and A046368 are subsequences. - Reinhard Zumkeller, Apr 11 2011

			10 = 2 * 5 is a term since both 2 and 5 are palindromes.
110 = 2 * 5 * 11 is a term since 2, 5 and 11 are palindromes.

Ivan Neretin, Table of n, a(n) for n = 1..10550
Index entries sequences related to prime factors

Cf. A002113, A002385, A046368, A051038.

a033620 n = a033620_list !! (n-1)
a033620_list = filter chi [1..] where
   chi n = a136522 spf == 1 && (n' == 1 || chi n') where
      n' = n `div` spf
      spf = a020639 n  -- cf. A020639
-- Reinhard Zumkeller, Apr 11 2011

N:= 5: # to get all terms of up to N digits
digrev:= proc(t) local L; L:= convert(t,base,10);
add(L[-i-1]*10^i,i=0..nops(L)-1);
end proc:
PPrimes:= [2,3,5,7,11]:
for d from 3 to N by 2 do
    m:= (d-1)/2;
    PPrimes:= PPrimes, select(isprime,[seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1)]);
od:
PPrimes:= map(op,[PPrimes]):
M:= 10^N:
B:= Vector(M);
B[1]:= 1:
for p in PPrimes do
  for k from 1 to floor(log[p](M)) do
     R:= [$1..floor(M/p^k)];
     B[p^k*R] := B[p^k*R] + B[R]
  od
od:
select(t -> B[t] > 0, [$1..M]); # Robert Israel, Jul 05 2015
# alternative
isA033620:= proc(n)
    for d in numtheory[factorset](n) do
        if not isA002113(op(1,d)) then
            return false;
        end if;
    end do;
    true ;
end proc:
for n from 1 to 300 do
    if isA033620(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Sep 09 2015

palQ[n_]:=Reverse[x=IntegerDigits[n]]==x; Select[Range[131],And@@palQ/@First/@FactorInteger[#]&] (* Jayanta Basu, Jun 05 2013 *)

ispal(n)=n=digits(n);for(i=1,#n\2,if(n[i]!=n[#n+1-i],return(0)));1
is(n)=if(n<13,n>0,vecmin(apply(ispal,factor(n)[,1]))) \\ Charles R Greathouse IV, Feb 06 2013

from sympy import isprime, primefactors
def pal(n): s = str(n); return s == s[::-1]
def ok(n): return all(pal(f) for f in primefactors(n))
print(list(filter(ok, range(1, 132)))) # Michael S. Branicky, Apr 06 2021

Sum_{n>=1} 1/a(n) = Product_{p in A002385} p/(p-1) = 5.0949... - Amiram Eldar, Sep 27 2020

A050782 Smallest positive multiplier m such that m*n is palindromic (or zero if no such m exists).

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 21, 38, 18, 35, 17, 16, 14, 9, 0, 12, 1, 7, 29, 21, 19, 37, 9, 8, 0, 14, 66, 1, 8, 15, 7, 3, 13, 15, 0, 16, 6, 23, 1, 13, 9, 3, 44, 7, 0, 19, 13, 4, 518, 1, 11, 3, 4, 13, 0, 442, 7, 4, 33, 9, 1, 11, 4, 6, 0, 845, 88, 4, 3, 7, 287, 1, 11, 6, 0, 12345679, 8

Offset: 0

Patrick De Geest, Oct 15 1999

Multiples of 81 require the largest multipliers.
From Jon E. Schoenfield, Jan 15 2015: (Start)
In general, a(n) is large when n is a multiple of 81. E.g., for n in [1..10000], of the 9000 terms where a(n)>0, 111 are at indices n that are multiples of 81; of the remaining 8889 terms,
     755 are in [1..9],
    1760 are in [10..99],
    3439 are in [100..999],
    2180 are in [1000..9999],
     708 are in [10000..99999],
      36 are in [100000..999999],
       6 are in [1000000..9999999],
       2 are in [10000000..99999999],
       2 are in [100000000..999999999],
and 1 (the largest) is a(8891) = 8546948927,
but the smallest of the 111 terms whose indices are multiples of 81 is a(2997)=333667. (End)
a(n) = 0 iff 10 | n. a(n) = 1 iff n is a palindrome. If k | a(n) then a(k*n) = a(n)/k. - Robert Israel, Jan 15 2015

			E.g., a(81) -> 81 * 12345679 = 999999999 and a palindrome.

Giovanni Resta, Table of n, a(n) for n = 0..10000 (first 8181 terms from Chai Wah Wu)
Patrick De Geest, World!Of Numbers

Cf. A002113, A020485, A050810.

digrev:= proc(n) local L,d,i;
  L:= convert(n,base,10);
  d:= nops(L);
  add(L[i]*10^(d-i),i=1..d);
end proc:
f:= proc(n)
local d,d2,x,t,y;
if n mod 10 = 0 then return 0 fi;
if n < 10 then return 1 fi;
for d from 2 do
  if d::even then
    d2:= d/2;
    for x from 10^(d2-1) to 10^d2-1 do
       t:= x*10^d2 + digrev(x);
       if t mod n = 0 then return(t/n) fi;
    od
  else
    d2:= (d-1)/2;
    for x from 10^(d2-1) to 10^d2-1 do
      for y from 0 to 9 do
        t:= x*10^(d2+1)+y*10^d2+digrev(x);
        if t mod n = 0 then return(t/n) fi;
      od
    od
  fi
od;
end proc:
seq(f(n),n=0 .. 100); # Robert Israel, Jan 15 2015

t={0}; Do[i=1; If[IntegerQ[n/10],y=0,While[Reverse[x=IntegerDigits[i*n]]!=x,i++]; y=i]; AppendTo[t,y],{n,80}]; t (* Jayanta Basu, Jun 01 2013 *)

from _future_ import division
def palgen(l,b=10): # generator of palindromes in base b of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1,l+1):
            n = b**(x-1)
            n2 = n*b
            for y in range(n,n2):
                k, m = y//b, 0
                while k >= b:
                    k, r = divmod(k,b)
                    m = b*m + r
                yield y*n + b*m + k
            for y in range(n,n2):
                k, m = y, 0
                while k >= b:
                    k, r = divmod(k,b)
                    m = b*m + r
                yield y*n2 + b*m + k
def A050782(n, l=10):
    if n % 10:
        x = palgen(l)
        next(x)  # replace with x.next() in Python 2.x
        for i in x:
            q, r = divmod(i, n)
            if not r:
                return q
        else:
            return 'search limit reached.'
    else:
        return 0 # Chai Wah Wu, Dec 30 2014

A261422 Number of ordered triples (u,v,w) of palindromes such that u+v+w=n.

Original entry on oeis.org

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 63, 72, 79, 84, 87, 88, 87, 84, 79, 72, 66, 55, 51, 45, 40, 36, 33, 31, 30, 30, 30, 33, 27, 34, 33, 33, 33, 33, 33, 33, 33, 33, 36, 27, 39, 36, 36, 36, 36, 36, 36, 36, 36, 39, 27, 45, 39, 39, 39, 39, 39, 39, 39, 39, 42, 27, 52, 42, 42, 42, 42, 42, 42, 42, 42, 45

Offset: 0

N. J. A. Sloane, Aug 27 2015

It is known that a(n)>0 for all n.

			4 can be written as a sum of three palindromes in 15 ways: 4+0+0 (3 ways), 3+1+0 (6 ways), 2+2+0 (3 ways), and 2+1+1 (3 ways), so a(4)=15.

N. J. A. Sloane, Table of n, a(n) for n = 0..10000 (See also the extended file with 200000 terms below)
William D. Banks, Every natural number is the sum of forty-nine palindromes, arXiv:1508.04721 [math.NT], 2015. [Establishes the much weaker result that the coefficients of P(x)^49 are positive (see Formula section below).]
Javier Cilleruelo and Florian Luca, Every positive integer is a sum of three palindromes, arXiv: 1602.06208 [math.NT], 2016-2017.
Erich Friedman, Problem of the Month (June 1999)
N. J. A. Sloane, Table of n, a(n) for n=0..200000
N. J. A. Sloane, Maple program to produce 200000 terms

Cf. A002113. Differs from A261132, which assumes 0 <= u <= v <= w.

For records see A262544, A262545.

(* This program is not suitable to compute a large number of terms. *)
compositions[n_, k_] := Flatten[Permutations[PadLeft[#, k]]& /@ IntegerPartitions[n, k], 1];
a[n_] := Select[compositions[n, 3], AllTrue[#, PalindromeQ]&] // Length;
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Aug 05 2018 *)

G.f. = P(x)^3, where P(x) = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^11 + x^22 + x^33 + x^44 + x^55 + x^66 + x^77 + x^88 + x^99 + x^101 + x^111 + ... = Sum_{palindromes p} x^p.

A331191 Numbers whose dual Zeckendorf representations (A104326) are palindromic.

Original entry on oeis.org

0, 1, 3, 4, 6, 11, 12, 16, 19, 22, 32, 33, 38, 42, 48, 53, 64, 71, 87, 88, 98, 106, 110, 118, 124, 134, 142, 148, 174, 194, 205, 231, 232, 245, 255, 271, 284, 288, 304, 317, 323, 336, 346, 362, 375, 402, 420, 462, 474, 516, 548, 566, 608, 609, 635, 656, 666, 687

Offset: 1

Amiram Eldar, Jan 11 2020

Pairs of numbers of the form {F(2*k-1)-2, F(2*k-1)-1}, for k >= 2, where F(k) is the k-th Fibonacci number, are consecutive terms in this sequence: {0, 1}, {3, 4}, {11, 12}, {32, 33}, ... - Amiram Eldar, Sep 03 2022

			4 is a term since its dual Zeckendorf representation, 101, is palindromic.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000045, A002113, A006995, A014190, A094202, A104326.

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 = Join[{{}}, Rest[Select[IntegerDigits[Range[0, 2^6 - 1], 2], SequenceCount[#, {0, 0}] == 0 &]]];
Union@Join[{0}, fib /@ Join[mirror[#, {}] & /@ (select[pals, 0]), mirror[#, {0}] & /@ (select[pals, 0]), mirror[#, {1}] & /@ pals]]

A008509 Positive integers k such that k-th triangular number is palindromic.

Original entry on oeis.org

1, 2, 3, 10, 11, 18, 34, 36, 77, 109, 132, 173, 363, 1111, 1287, 1593, 1833, 2662, 3185, 3369, 3548, 8382, 11088, 18906, 50281, 57166, 102849, 111111, 167053, 179158, 246642, 337650, 342270, 365436, 417972, 1620621, 3240425, 3457634, 3707883

Offset: 1

Patrick De Geest

Charles W. Trigg, Palindromic Triangular Numbers, J. Rec. Math., 6 (1973), 146-147.
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 93.

T. D. Noe, Table of n, a(n) for n = 1..147 (from P. De Geest)
P. De Geest, Palindromic Triangulars

Cf. A003098, A002113, A000217, A083571, A050721, A050722.

[k:k in [1..5000000]| Intseq(Binomial(k+1,2)) eq Reverse(Intseq(Binomial(k+1,2)))]; //  Marius A. Burtea, Jul 16 2019

palQ[n_]:= Reverse[x=IntegerDigits[n]]==x; t={}; Do[If[palQ[n*(n+1)/2],AppendTo[t,n]],{n,4*10^6}]; t (* Jayanta Basu, May 13 2013 *)
Position[Accumulate[Range[371*10^4]],?PalindromeQ]//Flatten (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale, Jun 12 2020 *)

ispal(n)=n=digits(n); for(i=1, #n\2, if(n[i]!=n[#n+1-i], return(0))); 1
is(n)=ispal(n*(n+1)/2) \\ Charles R Greathouse IV, May 15 2013

A032350 Palindromic nonprime numbers.

Original entry on oeis.org

1, 4, 6, 8, 9, 22, 33, 44, 55, 66, 77, 88, 99, 111, 121, 141, 161, 171, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 323, 333, 343, 363, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 606, 616

Offset: 1

Patrick De Geest

Complement of A002385 (palindromic primes) with respect to A002113 (palindromic numbers). - Jaroslav Krizek, Mar 12 2013

Banks, Hart, and Sakata derive a nontrivial upper bound for the number of prime palindromes n <= x as x tends to infinity. It follows that almost all palindromes are composite. The results hold in any base. The authors use Weil's bound for Kloosterman sums. - Jonathan Sondow, Jan 02 2018

Georg Fischer, Table of n, a(n) for n = 1..10217
W. D. Banks, D. N. Hart, and M. Sakata, Almost all palindromes are composite, Math. Res. Lett., 11 No. 5-6 (2004), 853-868.
Patrick De Geest, World!Of Numbers
Patrick De Geest, World!Of Palindromic Primes

Cf. A002113, A002385.

Filtered([1..620],n-> not IsPrime(n) and ListOfDigits(n)=Reversed(ListOfDigits(n))); # Muniru A Asiru, Mar 08 2019

palq[n_] := IntegerDigits[n]==Reverse[IntegerDigits[n]]; Select[Range[700], palq[ # ]&&!PrimeQ[ # ]&]
(* Second program: *)
Select[Range@ 616, And[PalindromeQ@ #, ! PrimeQ@ #] &] (* Michael De Vlieger, Jan 02 2018 *)

[n for n in (1..616) if not is_prime(n) and Word(n.digits()).is_palindrome()] # Peter Luschny, Sep 13 2018

Edited by Dean Hickerson, Oct 22 2002

cp's OEIS Frontend

A029953 Palindromic in base 6.

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A062687 Numbers all of whose divisors are palindromic.

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A055483 a(n) is the GCD of n and the reverse of n.

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A035137 Numbers that are not the sum of 2 palindromes (where 0 is considered a palindrome).

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A033620 Numbers all of whose prime factors are palindromes.

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A050782 Smallest positive multiplier m such that m*n is palindromic (or zero if no such m exists).

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