A329100 Composite palindromes whose divisors > 1 are all nontrivial palindromes (i.e., palindromes with at least two digits).

121, 1111, 1331, 1441, 1661, 1991, 3443, 3883, 7997, 10201, 12221, 13231, 14641, 15251, 15851, 18281, 19291, 31613, 35653, 37673, 37873, 38683, 112211, 113311, 115511, 116611, 124421, 125521, 134431, 136631, 139931, 145541, 146641, 157751, 167761, 169961, 176671

Offset: 1

Author

Maxim Veselov, Nov 04 2019

Keywords

• nonn
• base

Comments

This is the intersection of A062687 and A038511.

From Chai Wah Wu, Nov 08 2019 : (Start)

All terms start and end with the digits 1,3,7 or 9.

First term with 3 prime factors: 1331 = 11^3.

First term with 3 distinct prime factors: 145541 = 11*101*131.

First term with 4 prime factors: 14641 = 11^4.

First term with 5 prime factors: 1478741 = 11^4*101.

No term with more than 3 distinct prime factors or more than 5 prime factors among first 10000 terms.

(End)

Examples

			For k = 1331, its divisors > 1 are 11, 121 and 1331, all of which are palindromes with at least two digits, so 1331 is a term.
For k = 167761, its divisors > 1 are 11, 101, 151, 1111, 1661, 15251 and 167761, all of which are palindromes with at least two digits, so 167761 is a term.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008364, A038511, A062687.

Programs

Mathematica

aQ[n_] := CompositeQ[n] && AllTrue[Rest @ Divisors[n], # > 10 && PalindromeQ @ IntegerDigits[#] &]; Select[Range[200000], aQ] (* Amiram Eldar, Nov 06 2019 *)

PARI

isA329100(n) = if((n>1) && !isprime(n) && gcd(n,210)==1, {d = divisors(n); rd = vector(#d, i, subst(Polrev(digits(d[i])), x, 10)); (d == rd); }, 0) \\ Jianing Song, Nov 06 2019, based on the program of A062687

Extensions

More terms from Jianing Song, Nov 06 2019