A032350 -id:A032350 - cp's OEIS frontend

A222728 Palindromic composite numbers starting with a digit 7.

77, 707, 717, 737, 747, 767, 777, 7007, 7117, 7227, 7337, 7447, 7557, 7667, 7777, 7887, 7997, 70007, 70107, 70307, 70407, 70707, 70807, 70907, 71017, 71117, 71217, 71417, 71517, 71617, 71717, 71817, 72027, 72127, 72327, 72427, 72527, 72627, 72827, 72927, 73137

Offset: 1

Jaroslav Krizek, Mar 09 2013

Subsequence of A032350 (palindromic nonprime numbers) and A002113 (palindromic numbers). Complement of A222727 (palindromic primes starting with a digit 7) with respect to A043042 (palindromic numbers starting with a digit 7).

Jaroslav Krizek, Table of n, a(n) for n = 1..1038

Cf. A032350, A002113, A222727, A043042.

Table[Select[Range[7*10^d,8*10^d-1],CompositeQ[#]&&PalindromeQ[#]&],{d,4}]//Flatten (* Harvey P. Dale, Nov 07 2021 *)

A222729 Palindromic composite numbers starting with a digit 9.

Original entry on oeis.org

9, 99, 909, 939, 949, 959, 969, 979, 989, 999, 9009, 9119, 9229, 9339, 9449, 9559, 9669, 9779, 9889, 9999, 90009, 90109, 90209, 90309, 90409, 90509, 90609, 90809, 90909, 91119, 91219, 91319, 91419, 91519, 91619, 91719, 91819, 91919, 92029, 92129, 92229, 92329

Offset: 1

Jaroslav Krizek, Mar 03 2013

Subsequence of A032350 (palindromic nonprime numbers) and A002113 (palindromic numbers). Complement of A128375 (palindromic primes starting with a digit 9) with respect to A043044 (palindromic numbers starting with a digit 9).

Jaroslav Krizek, Table of n, a(n) for n = 1..1050

Cf. A032350, A002113, A128375, A043044.

Select[Range[100000],PalindromeQ[#]&&CompositeQ[#]&&IntegerDigits[#][[1]] == 9&] (* Harvey P. Dale, Oct 09 2021 *)

A046345 Sum of the prime factors of the palindromic composite numbers (counted with multiplicity).

Original entry on oeis.org

4, 5, 6, 6, 13, 14, 15, 16, 16, 18, 17, 17, 40, 22, 50, 30, 25, 103, 57, 42, 35, 24, 17, 133, 25, 52, 77, 104, 36, 43, 21, 25, 134, 105, 31, 59, 40, 44, 229, 37, 84, 26, 34, 106, 108, 20, 112, 114, 45, 118, 33, 24, 29, 106, 24, 315, 60, 38, 49, 45, 30, 23, 38, 108, 242, 78

Offset: 1

Patrick De Geest, Jun 15 1998

			a(60)=45 because 666 = 2 * 3 * 3 * 37 and 45 = 2 + 3 + 3 + 37.

Cf. A046343, A046344.

t={}; Do[If[!PrimeQ[n]&&Reverse[x=IntegerDigits[n]]==x,AppendTo[t,Total[Times@@@FactorInteger[n]]]],{n,4,740}]; t (* Jayanta Basu, Jun 04 2013 *)

a(n) = A001414(A032350(1+n)). - R. J. Mathar, Sep 09 2015

Offset set to 1. - R. J. Mathar, Sep 09 2015

A076609 Palindromic numbers with prime middle digit.

Original entry on oeis.org

2, 3, 5, 7, 121, 131, 151, 171, 222, 232, 252, 272, 323, 333, 353, 373, 424, 434, 454, 474, 525, 535, 555, 575, 626, 636, 656, 676, 727, 737, 757, 777, 828, 838, 858, 878, 929, 939, 959, 979, 10201, 10301, 10501, 10701, 11211, 11311, 11511, 11711, 12221

Offset: 1

Jani Melik, Oct 21 2002

There are no such with an even number of digits.

			a(12)=272=2^4*17 is palindromic number and its middle digit 7 is prime, a(13)=323=17*19 is palindromic number and its middle digit 2 is prime, a(14)=333=3^2*37 is palindromic number and its middle digit 3 is prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A032350, A056525.

ts_numprapal := proc(n) local ad,adr,midigit; ad := convert(n,base,10): adr := ListTools[Reverse](ad): if nops(ad) mod 2 = 0 then return 1; fi; midigit := op( (nops(ad)+1)/2,ad ): if (isprime( midigit )='true' and adr=ad) then return 0; else return 1; fi end: ts_num_pal := proc(i) if ts_numprapal(i) = 0 then return (i) fi end: anumpal := [seq(ts_num_pal(i), i=1..50000)]: anumpal;

pnpmdQ[n_]:=Module[{idn=IntegerDigits[n],len=IntegerLength[n]},OddQ[len] && PalindromeQ[n]&&PrimeQ[idn[[(len+1)/2]]]]; Select[Range[15000],pnpmdQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 08 2017 *)

A031880 Lucky numbers that are both palindromic and nonprime.

Original entry on oeis.org

1, 9, 33, 99, 111, 141, 171, 303, 393, 535, 717, 777, 979, 1441, 1771, 3003, 3223, 3663, 5335, 7447, 9009, 9339, 9999, 11011, 11811, 11911, 12121, 12321, 12621, 13531, 14041, 14541, 14841, 17671, 18381, 18681, 19791, 30303, 31713, 32223

Offset: 1

Patrick De Geest

Amiram Eldar, Table of n, a(n) for n = 1..5436 (terms below 10^9)

Intersection of A000959 and A032350.

Name corrected by Amiram Eldar, Nov 15 2019

A227947 Each term is a palindrome such that the sum of its proper divisors is a palindrome > 1.

Original entry on oeis.org

4, 6, 8, 9, 333, 646, 656, 979, 1001, 3553, 10801, 11111, 18581, 31713, 34943, 48484, 57375, 95259, 99099, 158851, 262262, 569965, 1173711, 1216121, 1399931, 1439341, 1502051, 1925291, 3203023, 3436343, 3659563, 3662663, 3803083, 3888883, 5185815, 5352535, 5893985, 5990995, 6902096, 9341439, 9452549

Offset: 1

Derek Orr, Oct 03 2013

All terms are composite numbers. - Chai Wah Wu, Dec 23 2015

			4 has proper divisors 1 and 2. 1 + 2 = 3 is also a palindrome. So 4 is a member of this sequence.

Chai Wah Wu, Table of n, a(n) for n = 1..220

Cf. A001065, A032350, A028986.

palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; fQ[n_] := Block[{s = DivisorSigma[1, n] - n}, palQ@ s && s > 1]; Select[
Select[Range@ 1000000, palQ], fQ] (* Michael De Vlieger, Apr 06 2015 *)
spdQ[n_]:=Module[{spd=DivisorSigma[1,n]-n},n==IntegerReverse[n] && spd>1 && spd==IntegerReverse[spd]]; Select[Range[10^7],spdQ] (* The program uses the IntegerReverse function from Mathematica version 10 *) (* Harvey P. Dale, Jan 03 2016 *)

pal(n)=d=digits(n);Vecrev(d)==d
for(n=1,10^6,s=sigma(n)-n;if(pal(n)&&pal(s)&&s>1,print1(n,", "))) \\ Derek Orr, Apr 05 2015

from sympy import divisors
def pal(n):
  r = ''
  for i in str(n):
    r = i + r
  return r == str(n)
{print(n,end=', ') for n in range(1,10**7) if pal(n) and pal(sum(divisors(n))-n) and len(divisors(n)) > 2}
## Simplified by Derek Orr, Apr 05 2015

Initial terms 0 and 1 removed and more terms added by Derek Orr, Apr 05 2015
Definition edited by Derek Orr, Apr 05 2015
Definition edited by Harvey P. Dale, Jan 03 2016

cp's OEIS Frontend

A222728 Palindromic composite numbers starting with a digit 7.

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A222729 Palindromic composite numbers starting with a digit 9.

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A046345 Sum of the prime factors of the palindromic composite numbers (counted with multiplicity).

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A076609 Palindromic numbers with prime middle digit.

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A031880 Lucky numbers that are both palindromic and nonprime.

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A227947 Each term is a palindrome such that the sum of its proper divisors is a palindrome > 1.

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