A110843 a(n) = least non-palindromic k such that k and r(k) have the same n prime divisors, where r(k) is the digit reversal of k.

1089, 2178, 21978, 24024, 2426424, 240264024, 23162643504, 2305213214304

Offset

2,1

Comments

Noting that a(6) = a(5)*(10^2+1) and a(7) = a(5)*(10^4+1), we can derive an upper bound for a(n), n>7, of 24024*(10^x+1), where x is the smallest power that gives the number (10^x+1) exactly (n-5) factors-greater-than-13. For n = {8, 9, 10, 11, 12, 13, 14, 15, 16}, this would be x = {10, 14, 16, 36, 30, 55, 45, 77, 70}. I think this upper limit exists for all n, so a(n) always exists. - Hans Havermann, Sep 26 2005

a(9) <= 2305213214304. a(10) <= 230316132350304. [From Donovan Johnson, Apr 09 2010]

The distinct prime factors of a(n) are a subset of the distinct prime factors of A056964(n). - David A. Corneth, Feb 15 2023

Links

Table of n, a(n) for n=2..9.

Example

a(3) = 2178 because 2178 and 8712 both have the same 3 prime divisors and 2178 is the least non-palindromic integer with this property.

Mathematica

r[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Do[k = 1; While[r[k] == k || Length[Select[Divisors[k], PrimeQ]] != n || Select[Divisors[k], PrimeQ] != Select[Divisors[r[k]], PrimeQ], k++ ]; Print[k], {n, 2, 10}]

Crossrefs

Cf. A056964.

Sequence in context: A110819 A071685 A008919 * A354256 A319570 A319482

Adjacent sequences: A110840 A110841 A110842 * A110844 A110845 A110846

Keyword

base,hard,nonn

Author

Ryan Propper, Sep 16 2005

Extensions

a(7) from Hans Havermann, Sep 26 2005

a(8) from Donovan Johnson, Apr 09 2010

a(9) from Michael S. Branicky, Feb 15 2023

Status

approved