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

1,1

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)

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A008364, A038511, A062687.

Sequence in context: A120353 A175983 A307858 * A208261 A036928 A088171

Adjacent sequences: A329097 A329098 A329099 * A329101 A329102 A329103

Keyword

nonn,base

Author

Maxim Veselov, Nov 04 2019

Extensions

More terms from Jianing Song, Nov 06 2019

Status

approved