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 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. 1
 1089, 2178, 21978, 24024, 2426424, 240264024, 23162643504, 2305213214304 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 6 01:58 EST 2023. Contains 367594 sequences. (Running on oeis4.)