

A110843


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


1




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 (n5) factorsgreaterthan13. 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



EXAMPLE

a(3) = 2178 because 2178 and 8712 both have the same 3 prime divisors and 2178 is the least nonpalindromic 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



KEYWORD

base,hard,nonn


AUTHOR



EXTENSIONS



STATUS

approved



